Mark Test 01 and Section Number on your scantron!
|
|
- Eugene Newton
- 5 years ago
- Views:
Transcription
1 FINAL EXAM ( min) MATH 65 SPRING 5 Student Name Student ID Instructor Section number (-digits, as in the table below) Mark Test and Section Number on your scantron! There are 5 questions on this exam. Each question is worth 8 points. Exam Rules. Students may not open the exam until instructed to do so.. Students must obey the orders and requests by all proctors, TAs, and lecturers.. No student may leave in the first min or in the last min of the exam. 4. Books, notes, calculators, or any electronic devices are not allowed on the exam, and they should not even be in sight in the exam room. Students may not look at anybody else s test, and may not communicate with anybody else except, if they have a question, with their TA or lecturer. 5. After time is called, the students have to put down all writing instruments and remain in their seats, while the TAs will collect the scantrons and the exams. 6. Any violation of these rules and any act of academic dishonesty may result in severe penalties. Additionally, all violators will be reported to the Office of the Dean of Students. I have read and understand the exam rules stated above: STUDENT SIGNATURE: Section Numbers: Bauman, Patricia: 7 Dadarlat, Marius: Gabrielov, Andrei: Ulrich, Bernd: Zhilan Julie Feng: 6 Noparstak, Jakob: 7 Ma, Linquan: (:am) and 7 (9:am) Li, Dan (:pm) and 5 (:pm) Kelleher, Daniel: (4:pm) and 4 (:pm) Gnang, Edinah (9:am) and 5 (:am) Xu, Xiang (MWF :pm) and 6 (MWF 4:pm) Zhang, Xu: 7 (TR :pm) and 7 (TR :pm)
2 () If we solve the equation: [ a + b c a c + a for a, b and c, the values of a and b are: = [ 4 A. a =, b = B. a = 7, b = 4 C. a = 5, b = D. a =, b = 4 E. There is no solution () Let A = Compute the (,) entry of AT A. A. 7 B. 4 C. D. 4 E. 4
3 () Which of the following sets of vectors span R? A. B. C. D. E. (4) Which of the following is a basis for the subspace of R spanned by S =? A. B. C. D. E.
4 (5) If L : R R is a linear transformation such that ([ ) ([ ) L =, L = then a + b + c is equal to: and ([ L ) = a b c, A. 8 B. C. 7 D. 4 E. 5 (6) If y = ax + b is the least square fit line for the points (, ), (, ), (, 4), find a + b. A. B. 7/ C. D. 5 E. 9/ 4
5 (7) Consider the matrix t t t A = t t, t where t is a real number. Then A is nonsingular if and only if A. t B. t and t C. t and t D. t, t, and t E. t is any real number (8) For a nonsingular 6 6 matrix A, the determinant of the adjoint matrix adj(a) is A. det(a) B. det(a 5 ) C. det(a 4 ) D. det(a ) E. det(a ) 5
6 (9) Let V be the set of all strictly positive numbers in R, and let and be defined by a b = ab, for any a, b in V (that is, a, b are strictly positive numbers), c a = a c, for any a in V and c in R. Which of the following statements are true? (i) For any a, b in V and any c in R, c (a b) belongs to V. (ii) Under the given operations, the element is the real number. (iii) There is at least one element a in V for which there is no element a such that ( a) a =. A. (i) only B. (ii) only C. (i) and (ii) only D. (i) and (iii) only E. All of them () Let S = {v, v, v }, where v = v = v =. Which of the following statements are true? (i) A basis for span S is {v, v }. (ii) The vector u = 4 belongs to span S. (iii) S is a linearly dependent set. A. (i) only B. (iii) only C. (i) and (iii) only D. (ii) and (iii) only E. All of them 6
7 () Let W be the vector space spanned by the vectors: u = [, u = [, u = [, u 4 = [. Apply the Gram-Schmidt process to the vectors u, u, u, u 4 (in this order) to find an orthonormal basis w, w, w, w 4 of W. What is w? A. [ B. [ C. [ / / D. [ / / E. [ / () Consider the subspace W of R 4 : W = span {[, [, [, [ 4 }. What is the dimension of W? A. B. C. D. E. 4 7
8 () Consider the homogeneous linear system a + b + c + 4d + 5e = a + c + e = b + c + d = Then the dimension of the solution space is A. B. C. D. E. 4 (4) Suppose A is a 5 matrix such that rank(a) =. Which of the following is TRUE? A. The rank of A T is 5 B. The nullity of A T is C. Ax = only has trivial solution D. The rows of A are linearly dependent E. The columns of A are linearly dependent 8
9 (5) The eigenvectors of [ are [ and If x (t), x (t) satisfy x () =, x () = and [ x (t) x = (t) compute x () + x (). [ with eigenvalues and respectively. [ [ x (t) x (t) A. 4e B. 4e e C. e e D. e e E. e 4e (6) The dimension of the vector space of all 4 4 symmetric matrices with real entries is equal to: A. 6 B. 8 C. 9 D. E. 9
10 (7) What is the characteristic polynomial of A = A. (λ )(λ + ) B. (λ )(λ )(λ + ) C. (λ )(λ + )(λ ) D. (λ )(λ + )(λ + ) E. (λ + )(λ + )(λ ) (8) Let A = P DP where P = Then A equals ( ) (, D = ) and P = ( ). ( ) 9 56 A ( ) 9 56 B ( ) 9 55 C ( ) 4 56 D ( ) 4 56 E. 5 55
11 (9) Find the eigenvalues and associated eigenvectors of the following matrix: [ A = 5 [ A. λ =, λ = 4, x = 5 [ B λ =, λ = 4, x = 5 [ C. λ =, λ = 4, x = 5 [ D. λ =, λ = 4, x = 5 [ E. λ =, λ = 4, x = 5 [, x =, x =, x =, x =, x = [ [ [ [ () Which of the following matrices is not diagonalizable? [ A. [ B. [ C. [ D. [ E.
12 () For which values of a does Gaussian elimination applied to a A = a a 4 a a a fail to give three pivots (leading s)? A.,, B.,, C.,, D.,, 4 E.,, 4 () If then b + c must be equal to: a b c A = has inverse A = a b c, a b c A. /4 B. 5/4 C. /4 D. /4 E. 7/4
13 [ + i () Let A =. Then A i is given by [ + i A. i [ i B. + i [ ( + i)/ / C. / ( i)/ [ i D. + i E. A does not exist. (4) Let u and v be orthogonal vectors in R 5 such that u = 7, v =. Then u v equals A. 9 B. C. 5 D. 7 E. 6
14 (5) Let A be a 7 matrix such that its null space is spanned by the vectors, and. The rank of A is: A. B. C. D. 4 E. 6 4
STUDENT NAME: STUDENT SIGNATURE: STUDENT ID NUMBER: SECTION NUMBER RECITATION INSTRUCTOR:
MA262 FINAL EXAM SPRING 2016 MAY 2, 2016 TEST NUMBER 01 INSTRUCTIONS: 1. Do not open the exam booklet until you are instructed to do so. 2. Before you open the booklet fill in the information below and
More informationMA EXAM 3 Form A April 16, You must use a #2 pencil on the mark sense sheet (answer sheet).
MA 16200 EXAM Form A April 16, 2015 NAME STUDENT ID # YOUR TA S NAME RECITATION TIME 1. You must use a #2 pencil on the mark sense sheet (answer sheet). 2. If the cover of your question booklet is GREEN,
More informationMA 265 FINAL EXAM Fall 2012
MA 265 FINAL EXAM Fall 22 NAME: INSTRUCTOR S NAME:. There are a total of 25 problems. You should show work on the exam sheet, and pencil in the correct answer on the scantron. 2. No books, notes, or calculators
More informationMA EXAM 3 Form A November 12, You must use a #2 pencil on the mark sense sheet (answer sheet).
MA 6200 EXAM 3 Form A November 2, 205 NAME STUDENT ID # YOUR TA S NAME RECITATION TIME. You must use a #2 pencil on the mark sense sheet (answer sheet). 2. If the cover of your question booklet is GREEN,
More informationSTUDENT NAME: STUDENT SIGNATURE: STUDENT ID NUMBER: SECTION NUMBER RECITATION INSTRUCTOR:
MA262 EXAM I SPRING 2016 FEBRUARY 25, 2016 TEST NUMBER 01 INSTRUCTIONS: 1. Do not open the exam booklet until you are instructed to do so. 2. Before you open the booklet fill in the information below and
More informationMA EXAM 1 Green February 8, You must use a #2 pencil on the mark sense sheet (answer sheet).
MA 16100 EXAM 1 Green February 8, 2016 NAME STUDENT ID # YOUR TA S NAME RECITATION TIME 1. You must use a #2 pencil on the mark sense sheet (answer sheet). 2. Be sure the paper you are looking at right
More informationMA FINAL EXAM Form 01 MAY 3, 2018
MA 16 FINAL EXAM Form 1 MAY, 18 NAME STUDENT ID # YOUR TA S NAME RECITATION TIME 1. You must use a # pencil on the scantron. a. Write 1 in the TEST/QUIZ NUMBER boxes and darken the appropriate bubbles
More informationMA EXAM 1 Form A February 4, You must use a #2 pencil on the mark sense sheet (answer sheet).
MA 162 EXAM 1 Form A February, 216 NAME STUDENT ID # YOUR TA S NAME RECITATION TIME 1. You must use a #2 pencil on the mark sense sheet (answer sheet). 2. If the cover of your question booklet is GREEN,
More informationCheck that your exam contains 30 multiple-choice questions, numbered sequentially.
MATH EXAM SPRING VERSION A NAME STUDENT NUMBER INSTRUCTOR SECTION NUMBER On your scantron, write and bubble your PSU ID, Section Number, and Test Version. Failure to correctly code these items may result
More informationMA EXAM 3 Green April 11, You must use a #2 pencil on the mark sense sheet (answer sheet).
MA 600 EXAM Green April, 206 NAME STUDENT ID # YOUR TA S NAME RECITATION TIME. You must use a #2 pencil on the mark sense sheet (answer sheet). 2. Be sure the paper you are looking at right now is GREEN!.
More informationMA 262, Fall 2017, Final Version 01(Green)
INSTRUCTIONS MA 262, Fall 2017, Final Version 01(Green) (1) Switch off your phone upon entering the exam room. (2) Do not open the exam booklet until you are instructed to do so. (3) Before you open the
More informationMA FINAL EXAM Green May 5, You must use a #2 pencil on the mark sense sheet (answer sheet).
MA 600 FINAL EXAM Green May 5, 06 NAME STUDENT ID # YOUR TA S NAME RECITATION TIME. You must use a # pencil on the mark sense sheet (answer sheet).. Be sure the paper you are looking at right now is GREEN!
More informationMA 161 EXAM 3 GREEN November 14, You must use a #2 pencil on the scantron sheet (answer sheet).
MA 161 EXAM 3 GREEN November 14, 2016 NAME STUDENT ID # YOUR TA S NAME RECITATION TIME 1. You must use a #2 pencil on the scantron sheet (answer sheet). 2. Be sure the paper you are looking at right now
More informationMath 2114 Common Final Exam May 13, 2015 Form A
Math 4 Common Final Exam May 3, 5 Form A Instructions: Using a # pencil only, write your name and your instructor s name in the blanks provided. Write your student ID number and your CRN in the blanks
More informationReduction to the associated homogeneous system via a particular solution
June PURDUE UNIVERSITY Study Guide for the Credit Exam in (MA 5) Linear Algebra This study guide describes briefly the course materials to be covered in MA 5. In order to be qualified for the credit, one
More informationMA FINAL EXAM Form A December 16, You must use a #2 pencil on the mark sense sheet (answer sheet).
MA 600 FINAL EXAM Form A December 6, 05 NAME STUDENT ID # YOUR TA S NAME RECITATION TIME. You must use a # pencil on the mark sense sheet (answer sheet).. If the cover of your question booklet is GREEN,
More informationMA FINAL EXAM Green December 16, You must use a #2 pencil on the mark sense sheet (answer sheet).
MA 600 FINAL EXAM Green December 6, 205 NAME STUDENT ID # YOUR TA S NAME RECITATION TIME. You must use a #2 pencil on the mark sense sheet (answer sheet). 2. Be sure the paper you are looking at right
More informationMA 161 Final Exam December 13, You must use a #2 pencil on the scantron sheet (answer sheet).
MA 161 Final Exam December 1, 016 NAME STUDENT ID # YOUR TA S NAME RECITATION TIME 1. You must use a # pencil on the scantron sheet (answer sheet).. Write the following in the TEST/QUIZ NUMBER boxes (and
More informationLINEAR ALGEBRA 1, 2012-I PARTIAL EXAM 3 SOLUTIONS TO PRACTICE PROBLEMS
LINEAR ALGEBRA, -I PARTIAL EXAM SOLUTIONS TO PRACTICE PROBLEMS Problem (a) For each of the two matrices below, (i) determine whether it is diagonalizable, (ii) determine whether it is orthogonally diagonalizable,
More informationMATH 31 - ADDITIONAL PRACTICE PROBLEMS FOR FINAL
MATH 3 - ADDITIONAL PRACTICE PROBLEMS FOR FINAL MAIN TOPICS FOR THE FINAL EXAM:. Vectors. Dot product. Cross product. Geometric applications. 2. Row reduction. Null space, column space, row space, left
More informationMath 265 Linear Algebra Sample Spring 2002., rref (A) =
Math 265 Linear Algebra Sample Spring 22. It is given that A = rref (A T )= 2 3 5 3 2 6, rref (A) = 2 3 and (a) Find the rank of A. (b) Find the nullityof A. (c) Find a basis for the column space of A.
More informationMA EXAM 1 INSTRUCTIONS VERSION 01 September 13, Section # and recitation time
MA 16200 EXAM 1 INSTRUCTIONS VERSION 01 September 13, 2018 Your name Student ID # Your TA s name Section # and recitation time 1. You must use a #2 pencil on the scantron sheet (answer sheet). 2. Check
More informationMath 18, Linear Algebra, Lecture C00, Spring 2017 Review and Practice Problems for Final Exam
Math 8, Linear Algebra, Lecture C, Spring 7 Review and Practice Problems for Final Exam. The augmentedmatrix of a linear system has been transformed by row operations into 5 4 8. Determine if the system
More informationPart I True or False. (One point each. A wrong answer is subject to one point deduction.)
FACULTY OF ENGINEERING CHULALONGKORN UNIVERSITY 21121 Computer Engineering Mathematics YEAR II, Second Semester, Final Examination, March 3, 214, 13: 16: Name ID 2 1 CR58 Instructions 1. There are 43 questions,
More informationMATH 240 Spring, Chapter 1: Linear Equations and Matrices
MATH 240 Spring, 2006 Chapter Summaries for Kolman / Hill, Elementary Linear Algebra, 8th Ed. Sections 1.1 1.6, 2.1 2.2, 3.2 3.8, 4.3 4.5, 5.1 5.3, 5.5, 6.1 6.5, 7.1 7.2, 7.4 DEFINITIONS Chapter 1: Linear
More informationMATH 20F: LINEAR ALGEBRA LECTURE B00 (T. KEMP)
MATH 20F: LINEAR ALGEBRA LECTURE B00 (T KEMP) Definition 01 If T (x) = Ax is a linear transformation from R n to R m then Nul (T ) = {x R n : T (x) = 0} = Nul (A) Ran (T ) = {Ax R m : x R n } = {b R m
More informationMA FINAL EXAM Form A MAY 1, 2017
MA 6 FINAL EXAM Form A MAY, 7 NAME STUDENT ID # YOUR TA S NAME RECITATION TIME. You must use a # pencil on the scantron. a. If the cover of your exam is GREEN, write in the TEST/QUIZ NUMBER boxes and darken
More informationMA FINAL EXAM Form B December 13, 2016
MA 6100 FINAL EXAM Form B December 1, 016 NAME STUDENT ID # YOUR TA S NAME RECITATION TIME 1. You must use a # pencil on the scantron. a. If the cover of your exam is GREEN, write 01 in the TEST/QUIZ NUMBER
More informationMA EXAM 2 INSTRUCTIONS VERSION 01 March 9, Section # and recitation time
MA 16600 EXAM INSTRUCTIONS VERSION 01 March 9, 016 Your name Student ID # Your TA s name Section # and recitation time 1. You must use a # pencil on the scantron sheet (answer sheet).. Check that the cover
More information1. What is the determinant of the following matrix? a 1 a 2 4a 3 2a 2 b 1 b 2 4b 3 2b c 1. = 4, then det
What is the determinant of the following matrix? 3 4 3 4 3 4 4 3 A 0 B 8 C 55 D 0 E 60 If det a a a 3 b b b 3 c c c 3 = 4, then det a a 4a 3 a b b 4b 3 b c c c 3 c = A 8 B 6 C 4 D E 3 Let A be an n n matrix
More informationI. Multiple Choice Questions (Answer any eight)
Name of the student : Roll No : CS65: Linear Algebra and Random Processes Exam - Course Instructor : Prashanth L.A. Date : Sep-24, 27 Duration : 5 minutes INSTRUCTIONS: The test will be evaluated ONLY
More informationMA FINAL EXAM Form 01 May 1, 2017
MA 26100 FINAL EXAM Form 01 May 1, 2017 NAME STUDENT ID # YOUR TA S NAME RECITATION TIME 1. You must use a #2 pencil on the scantron 2. a. Write 01 in the TEST/QUIZ NUMBER boxes and darken the appropriate
More informationSTUDENT NAME: STUDENT SIGNATURE: STUDENT ID NUMBER: SECTION NUMBER AND RECITATION INSTRUCTOR:
MA66 EXAM II SPRING 09 MARCH 5, 09 TEST NUMBER INSTRUCTIONS:. Do not open the exam booklet until you are instructed to do so.. Before you open the booklet fill in the information below and use a # pencil
More informationMATH 1120 (LINEAR ALGEBRA 1), FINAL EXAM FALL 2011 SOLUTIONS TO PRACTICE VERSION
MATH (LINEAR ALGEBRA ) FINAL EXAM FALL SOLUTIONS TO PRACTICE VERSION Problem (a) For each matrix below (i) find a basis for its column space (ii) find a basis for its row space (iii) determine whether
More informationMA EXAM 3 INSTRUCTIONS VERSION 01 April 18, Section # and recitation time
MA 16600 EXAM 3 INSTRUCTIONS VERSION 01 April 18, 2018 Your name Student ID # Your TA s name Section # and recitation time 1. You must use a #2 pencil on the scantron sheet (answer sheet). 2. Check that
More informationProblem # Max points possible Actual score Total 120
FINAL EXAMINATION - MATH 2121, FALL 2017. Name: ID#: Email: Lecture & Tutorial: Problem # Max points possible Actual score 1 15 2 15 3 10 4 15 5 15 6 15 7 10 8 10 9 15 Total 120 You have 180 minutes to
More informationMA EXAM 3 INSTRUCTIONS VERSION 01 April 17, Section # and recitation time
MA 16600 EXAM 3 INSTRUCTIONS VERSION 01 April 17, 2014 Your name Student ID # Your TA s name Section # and recitation time 1. You must use a #2 pencil on the scantron sheet (answer sheet). 2. Check that
More informationMA Exam 1 Fall 2015 VERSION 01
VERSION 01 Your name Student ID # Section # and recitation time 1. You must use a # pencil on the scantron sheet (answer sheet).. Check that the cover of your Question Booklet is GREEN and that it has
More informationMA EXAM 3 INSTRUCTIONS VERSION 01 April 14, Section # and recitation time
MA 16600 EXAM 3 INSTRUCTIONS VERSION 01 April 14, 2015 Your name Student ID # Your TA s name Section # and recitation time 1. You must use a #2 pencil on the scantron sheet (answer sheet). 2. Check that
More informationMA 262, Spring 2018, Midterm 1 Version 01 (Green)
MA 262, Spring 2018, Midterm 1 Version 01 (Green) INSTRUCTIONS 1. Switch off your phone upon entering the exam room. 2. Do not open the exam booklet until you are instructed to do so. 3. Before you open
More informationSTUDENT NAME: STUDENT SIGNATURE: STUDENT ID NUMBER: SECTION NUMBER AND RECITATION INSTRUCTOR:
MA166 EXAM I SPRING 2019 FEBRUARY 5, 2019 TEST NUMBER 22 INSTRUCTIONS: 1. Do not open the exam booklet until you are instructed to do so. 2. Before you open the booklet fill in the information below and
More informationEK102 Linear Algebra PRACTICE PROBLEMS for Final Exam Spring 2016
EK102 Linear Algebra PRACTICE PROBLEMS for Final Exam Spring 2016 Answer the questions in the spaces provided on the question sheets. You must show your work to get credit for your answers. There will
More information1. Let m 1 and n 1 be two natural numbers such that m > n. Which of the following is/are true?
. Let m and n be two natural numbers such that m > n. Which of the following is/are true? (i) A linear system of m equations in n variables is always consistent. (ii) A linear system of n equations in
More informationTHE USE OF A CALCULATOR, CELL PHONE, OR ANY OTHER ELEC- TRONIC DEVICE IS NOT PERMITTED DURING THIS EXAMINATION.
MATH FINAL EXAM DECEMBER 8, 7 FORM A NAME STUDENT NUMBER INSTRUCTOR SECTION NUMBER This examination will be machine processed by the University Testing Service. Use only a number pencil on your answer
More informationMA EXAM 2 INSTRUCTIONS VERSION 01 March 10, Section # and recitation time
MA 66 EXAM INSTRUCTIONS VERSION March, Your name Student ID # Your TA s name Section # and recitation time. You must use a # pencil on the scantron sheet (answer sheet).. Check that the cover of your question
More informationMATH 304 Linear Algebra Lecture 34: Review for Test 2.
MATH 304 Linear Algebra Lecture 34: Review for Test 2. Topics for Test 2 Linear transformations (Leon 4.1 4.3) Matrix transformations Matrix of a linear mapping Similar matrices Orthogonality (Leon 5.1
More informationMA162 EXAM III SPRING 2017 APRIL 11, 2017 TEST NUMBER 01 INSTRUCTIONS:
MA62 EXAM III SPRING 207 APRIL, 207 TEST NUMBER 0 INSTRUCTIONS:. Do not open the exam booklet until you are instructed to do so. 2. Before you open the booklet fill in the information below and use a #
More information5.) For each of the given sets of vectors, determine whether or not the set spans R 3. Give reasons for your answers.
Linear Algebra - Test File - Spring Test # For problems - consider the following system of equations. x + y - z = x + y + 4z = x + y + 6z =.) Solve the system without using your calculator..) Find the
More informationMath 2174: Practice Midterm 1
Math 74: Practice Midterm Show your work and explain your reasoning as appropriate. No calculators. One page of handwritten notes is allowed for the exam, as well as one blank page of scratch paper.. Consider
More informationMA EXAM 3 INSTRUCTIONS VERSION 01 November 8, Section # and recitation time
MA 16500 EXAM 3 INSTRUCTIONS VERSION 01 November 8, 2016 Your name Student ID # Your TA s name Section # and recitation time 1. You must use a #2 pencil on the scantron sheet (answer sheet). 2. Check that
More information1. Select the unique answer (choice) for each problem. Write only the answer.
MATH 5 Practice Problem Set Spring 7. Select the unique answer (choice) for each problem. Write only the answer. () Determine all the values of a for which the system has infinitely many solutions: x +
More informationMA EXAM 1 INSTRUCTIONS VERSION 01 FEBRUARY 8, Section # and recitation time
MA 16600 EXAM 1 INSTRUCTIONS VERSION 01 FEBRUARY 8, 2017 Your name Student ID # Your TA s name Section # and recitation time 1. You must use a #2 pencil on the scantron sheet (answer sheet). 2. Check that
More informationMATH. 20F SAMPLE FINAL (WINTER 2010)
MATH. 20F SAMPLE FINAL (WINTER 2010) You have 3 hours for this exam. Please write legibly and show all working. No calculators are allowed. Write your name, ID number and your TA s name below. The total
More informationFall 2016 MATH*1160 Final Exam
Fall 2016 MATH*1160 Final Exam Last name: (PRINT) First name: Student #: Instructor: M. R. Garvie Dec 16, 2016 INSTRUCTIONS: 1. The exam is 2 hours long. Do NOT start until instructed. You may use blank
More informationLast name: First name: Signature: Student number:
MAT 2141 The final exam Instructor: K. Zaynullin Last name: First name: Signature: Student number: Do not detach the pages of this examination. You may use the back of the pages as scrap paper for calculations,
More informationMath 323 Exam 2 Sample Problems Solution Guide October 31, 2013
Math Exam Sample Problems Solution Guide October, Note that the following provides a guide to the solutions on the sample problems, but in some cases the complete solution would require more work or justification
More information2. Every linear system with the same number of equations as unknowns has a unique solution.
1. For matrices A, B, C, A + B = A + C if and only if A = B. 2. Every linear system with the same number of equations as unknowns has a unique solution. 3. Every linear system with the same number of equations
More informationI have read and understood the instructions regarding academic dishonesty:
Name Final Exam MATH 6600 SPRING 08 MARK TEST 0 ON YOUR SCANTRON! Student ID Section Number (see list below 03 UNIV 03 0:30am TR Alper, Onur 04 REC 3:30pm MWF Luo, Tao 05 UNIV 03 :30pm TR Hora, Raphael
More information235 Final exam review questions
5 Final exam review questions Paul Hacking December 4, 0 () Let A be an n n matrix and T : R n R n, T (x) = Ax the linear transformation with matrix A. What does it mean to say that a vector v R n is an
More informationYORK UNIVERSITY. Faculty of Science Department of Mathematics and Statistics MATH M Test #2 Solutions
YORK UNIVERSITY Faculty of Science Department of Mathematics and Statistics MATH 3. M Test # Solutions. (8 pts) For each statement indicate whether it is always TRUE or sometimes FALSE. Note: For this
More informationGlossary of Linear Algebra Terms. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Glossary of Linear Algebra Terms Basis (for a subspace) A linearly independent set of vectors that spans the space Basic Variable A variable in a linear system that corresponds to a pivot column in the
More informationSpring 2014 Math 272 Final Exam Review Sheet
Spring 2014 Math 272 Final Exam Review Sheet You will not be allowed use of a calculator or any other device other than your pencil or pen and some scratch paper. Notes are also not allowed. In kindness
More informationColumbus State Community College Mathematics Department Public Syllabus
Columbus State Community College Mathematics Department Public Syllabus Course and Number: MATH 2568 Elementary Linear Algebra Credits: 4 Class Hours Per Week: 4 Prerequisites: MATH 2153 with a C or higher
More informationCheck that your exam contains 20 multiple-choice questions, numbered sequentially.
MATH 22 MAKEUP EXAMINATION Fall 26 VERSION A NAME STUDENT NUMBER INSTRUCTOR SECTION NUMBER On your scantron, write and bubble your PSU ID, Section Number, and Test Version. Failure to correctly code these
More informationMath 224, Fall 2007 Exam 3 Thursday, December 6, 2007
Math 224, Fall 2007 Exam 3 Thursday, December 6, 2007 You have 1 hour and 20 minutes. No notes, books, or other references. You are permitted to use Maple during this exam, but you must start with a blank
More informationMath 314/ Exam 2 Blue Exam Solutions December 4, 2008 Instructor: Dr. S. Cooper. Name:
Math 34/84 - Exam Blue Exam Solutions December 4, 8 Instructor: Dr. S. Cooper Name: Read each question carefully. Be sure to show all of your work and not just your final conclusion. You may not use your
More informationft-uiowa-math2550 Assignment OptionalFinalExamReviewMultChoiceMEDIUMlengthForm due 12/31/2014 at 10:36pm CST
me me ft-uiowa-math255 Assignment OptionalFinalExamReviewMultChoiceMEDIUMlengthForm due 2/3/2 at :3pm CST. ( pt) Library/TCNJ/TCNJ LinearSystems/problem3.pg Give a geometric description of the following
More informationDIAGONALIZATION. In order to see the implications of this definition, let us consider the following example Example 1. Consider the matrix
DIAGONALIZATION Definition We say that a matrix A of size n n is diagonalizable if there is a basis of R n consisting of eigenvectors of A ie if there are n linearly independent vectors v v n such that
More informationPRACTICE PROBLEMS FOR THE FINAL
PRACTICE PROBLEMS FOR THE FINAL Here are a slew of practice problems for the final culled from old exams:. Let P be the vector space of polynomials of degree at most. Let B = {, (t ), t + t }. (a) Show
More informationMath 308 Practice Test for Final Exam Winter 2015
Math 38 Practice Test for Final Exam Winter 25 No books are allowed during the exam. But you are allowed one sheet ( x 8) of handwritten notes (back and front). You may use a calculator. For TRUE/FALSE
More informationPractice Final Exam. Solutions.
MATH Applied Linear Algebra December 6, 8 Practice Final Exam Solutions Find the standard matrix f the linear transfmation T : R R such that T, T, T Solution: Easy to see that the transfmation T can be
More informationMath 102, Winter Final Exam Review. Chapter 1. Matrices and Gaussian Elimination
Math 0, Winter 07 Final Exam Review Chapter. Matrices and Gaussian Elimination { x + x =,. Different forms of a system of linear equations. Example: The x + 4x = 4. [ ] [ ] [ ] vector form (or the column
More informationPreliminary/Qualifying Exam in Numerical Analysis (Math 502a) Spring 2012
Instructions Preliminary/Qualifying Exam in Numerical Analysis (Math 502a) Spring 2012 The exam consists of four problems, each having multiple parts. You should attempt to solve all four problems. 1.
More informationPRACTICE FINAL EXAM. why. If they are dependent, exhibit a linear dependence relation among them.
Prof A Suciu MTH U37 LINEAR ALGEBRA Spring 2005 PRACTICE FINAL EXAM Are the following vectors independent or dependent? If they are independent, say why If they are dependent, exhibit a linear dependence
More informationMAT Linear Algebra Collection of sample exams
MAT 342 - Linear Algebra Collection of sample exams A-x. (0 pts Give the precise definition of the row echelon form. 2. ( 0 pts After performing row reductions on the augmented matrix for a certain system
More informationCheat Sheet for MATH461
Cheat Sheet for MATH46 Here is the stuff you really need to remember for the exams Linear systems Ax = b Problem: We consider a linear system of m equations for n unknowns x,,x n : For a given matrix A
More informationElementary Linear Algebra Review for Exam 2 Exam is Monday, November 16th.
Elementary Linear Algebra Review for Exam Exam is Monday, November 6th. The exam will cover sections:.4,..4, 5. 5., 7., the class notes on Markov Models. You must be able to do each of the following. Section.4
More informationMath 520 Exam 2 Topic Outline Sections 1 3 (Xiao/Dumas/Liaw) Spring 2008
Math 520 Exam 2 Topic Outline Sections 1 3 (Xiao/Dumas/Liaw) Spring 2008 Exam 2 will be held on Tuesday, April 8, 7-8pm in 117 MacMillan What will be covered The exam will cover material from the lectures
More informationhomogeneous 71 hyperplane 10 hyperplane 34 hyperplane 69 identity map 171 identity map 186 identity map 206 identity matrix 110 identity matrix 45
address 12 adjoint matrix 118 alternating 112 alternating 203 angle 159 angle 33 angle 60 area 120 associative 180 augmented matrix 11 axes 5 Axiom of Choice 153 basis 178 basis 210 basis 74 basis test
More informationMAT188H1S LINEAR ALGEBRA: Course Information as of February 2, Calendar Description:
MAT188H1S LINEAR ALGEBRA: Course Information as of February 2, 2019 2018-2019 Calendar Description: This course covers systems of linear equations and Gaussian elimination, applications; vectors in R n,
More information(Practice)Exam in Linear Algebra
(Practice)Exam in Linear Algebra May 016 First Year at The Faculties of Engineering and Science and of Health This test has 10 pages and 16 multiple-choice problems. In two-sided print. It is allowed to
More informationMATH 223 FINAL EXAM APRIL, 2005
MATH 223 FINAL EXAM APRIL, 2005 Instructions: (a) There are 10 problems in this exam. Each problem is worth five points, divided equally among parts. (b) Full credit is given to complete work only. Simply
More informationThe definition of a vector space (V, +, )
The definition of a vector space (V, +, ) 1. For any u and v in V, u + v is also in V. 2. For any u and v in V, u + v = v + u. 3. For any u, v, w in V, u + ( v + w) = ( u + v) + w. 4. There is an element
More informationMATH 304 Linear Algebra Lecture 20: The Gram-Schmidt process (continued). Eigenvalues and eigenvectors.
MATH 304 Linear Algebra Lecture 20: The Gram-Schmidt process (continued). Eigenvalues and eigenvectors. Orthogonal sets Let V be a vector space with an inner product. Definition. Nonzero vectors v 1,v
More informationMath 301 Final Exam. Dr. Holmes. December 17, 2007
Math 30 Final Exam Dr. Holmes December 7, 2007 The final exam begins at 0:30 am. It ends officially at 2:30 pm; if everyone in the class agrees to this, it will continue until 2:45 pm. The exam is open
More information0 2 0, it is diagonal, hence diagonalizable)
MATH 54 TRUE/FALSE QUESTIONS FOR MIDTERM 2 SOLUTIONS PEYAM RYAN TABRIZIAN 1. (a) TRUE If A is diagonalizable, then A 3 is diagonalizable. (A = P DP 1, so A 3 = P D 3 P = P D P 1, where P = P and D = D
More informationNo books, no notes, no calculators. You must show work, unless the question is a true/false, yes/no, or fill-in-the-blank question.
Math 304 Final Exam (May 8) Spring 206 No books, no notes, no calculators. You must show work, unless the question is a true/false, yes/no, or fill-in-the-blank question. Name: Section: Question Points
More informationQuizzes for Math 304
Quizzes for Math 304 QUIZ. A system of linear equations has augmented matrix 2 4 4 A = 2 0 2 4 3 5 2 a) Write down this system of equations; b) Find the reduced row-echelon form of A; c) What are the pivot
More informationLinear Algebra (MATH ) Spring 2011 Final Exam Practice Problem Solutions
Linear Algebra (MATH 4) Spring 2 Final Exam Practice Problem Solutions Instructions: Try the following on your own, then use the book and notes where you need help. Afterwards, check your solutions with
More informationMATH 220 FINAL EXAMINATION December 13, Name ID # Section #
MATH 22 FINAL EXAMINATION December 3, 2 Name ID # Section # There are??multiple choice questions. Each problem is worth 5 points. Four possible answers are given for each problem, only one of which is
More informationMath Final December 2006 C. Robinson
Math 285-1 Final December 2006 C. Robinson 2 5 8 5 1 2 0-1 0 1. (21 Points) The matrix A = 1 2 2 3 1 8 3 2 6 has the reduced echelon form U = 0 0 1 2 0 0 0 0 0 1. 2 6 1 0 0 0 0 0 a. Find a basis for the
More informationMath 4A Notes. Written by Victoria Kala Last updated June 11, 2017
Math 4A Notes Written by Victoria Kala vtkala@math.ucsb.edu Last updated June 11, 2017 Systems of Linear Equations A linear equation is an equation that can be written in the form a 1 x 1 + a 2 x 2 +...
More informationMATH 1553 SAMPLE FINAL EXAM, SPRING 2018
MATH 1553 SAMPLE FINAL EXAM, SPRING 2018 Name Circle the name of your instructor below: Fathi Jankowski Kordek Strenner Yan Please read all instructions carefully before beginning Each problem is worth
More informationMATH 2210Q MIDTERM EXAM I PRACTICE PROBLEMS
MATH Q MIDTERM EXAM I PRACTICE PROBLEMS Date and place: Thursday, November, 8, in-class exam Section : : :5pm at MONT Section : 9: :5pm at MONT 5 Material: Sections,, 7 Lecture 9 8, Quiz, Worksheet 9 8,
More informationSolutions to practice questions for the final
Math A UC Davis, Winter Prof. Dan Romik Solutions to practice questions for the final. You are given the linear system of equations x + 4x + x 3 + x 4 = 8 x + x + x 3 = 5 x x + x 3 x 4 = x + x + x 4 =
More informationMATH Spring 2011 Sample problems for Test 2: Solutions
MATH 304 505 Spring 011 Sample problems for Test : Solutions Any problem may be altered or replaced by a different one! Problem 1 (15 pts) Let M, (R) denote the vector space of matrices with real entries
More informationMath 415 Exam I. Name: Student ID: Calculators, books and notes are not allowed!
Math 415 Exam I Calculators, books and notes are not allowed! Name: Student ID: Score: Math 415 Exam I (20pts) 1. Let A be a square matrix satisfying A 2 = 2A. Find the determinant of A. Sol. From A 2
More informationSUMMARY OF MATH 1600
SUMMARY OF MATH 1600 Note: The following list is intended as a study guide for the final exam. It is a continuation of the study guide for the midterm. It does not claim to be a comprehensive list. You
More informationThe value of a problem is not so much coming up with the answer as in the ideas and attempted ideas it forces on the would be solver I.N.
Math 410 Homework Problems In the following pages you will find all of the homework problems for the semester. Homework should be written out neatly and stapled and turned in at the beginning of class
More informationDimension. Eigenvalue and eigenvector
Dimension. Eigenvalue and eigenvector Math 112, week 9 Goals: Bases, dimension, rank-nullity theorem. Eigenvalue and eigenvector. Suggested Textbook Readings: Sections 4.5, 4.6, 5.1, 5.2 Week 9: Dimension,
More information