ft-uiowa-math2550 Assignment Hw1fall14 due 09/03/2014 at 10:56pm CDT 3. (1 pt) Library/WHFreeman/Holt linear algebra/chaps 1-4- /holt
|
|
|
- Barry Carter
- 6 years ago
- Views:
Transcription
1 me me Assignment Hw1fall14 due 09/03/2014 at 10:56pm CDT ft-uiowa-math (1 pt) Library/WHFreeman/Holt linear algebra/chaps 1-4- /holt pg in echelon form, reduced row echelon form, or neither.?. not in echelon form 2. (1 pt) Library/WHFreeman/Holt linear algebra/chaps 1-4- /holt pg in echelon form, reduced row echelon form, or neither.?. reduced row echelon form Two lines intersecting in a point Two parallel lines Two lines that are the same 5. (1 pt) Library/TCNJ/TCNJ LinearSystems/problem1.pg 6x +5y = 5 4x +4y = 7 10x +11y = 23 10x +15y = 15 4x 6y = 6 12x 18y = 18 6x +5y = 5 4x +4y = 7 10x +11y = 25 Unique Solution 3. (1 pt) Library/WHFreeman/Holt linear algebra/chaps 1-4- /holt pg in echelon form, reduced row echelon form, or neither.?. reduced row echelon form 4. (1 pt) Library/TCNJ/TCNJ LinearSystems/problem11.pg Give a geometric description of the following systems of equations. 7x + 7y = 6 6x + 5y = 8 4x + 4y = 6 8x + 8y = 13 4x + 4y = 6 8x + 8y = (1 pt) Library/TCNJ/TCNJ LinearSystems/problem3.pg Give a geometric description of the following systems of equations 4x 16y = 4 3x + 12y = 3 7x + 28y = 7 x 3y = 5 2x 3y = 9 7x 9y = 31 x 3y = 5 2x 3y = 9 7x 9y = 28 Three identical lines Three lines intersecting at a single point Three non-parallel lines with no common intersection
2 7. (1 pt) Library/TCNJ/TCNJ LinearSystems/problem2.pg 10. (1 pt) Library/TCNJ/TCNJ LinearSystems/problem17.pg 7x + 2y + 6z = 3 9x + 5y + 7z = 10 15x 20y + 15z = 0 6x + 8y 6z = 3 15x 20y + 15z = 0 6x + 8y 6z = 0 8. (1 pt) Library/TCNJ/TCNJ LinearSystems/problem4.pg Give a geometric description of the following system of equations 2x + 4y 6z = 12 x + 5y 9z = 1 2x + 4y 6z = 12 3x 6y + 9z = 16 2x + 4y 6z = 12 3x 6y + 9z = 18 Two planes intersecting in a line Two parallel planes Two planes that are the same 9. (1 pt) Library/TCNJ/TCNJ LinearSystems/problem6.pg Give a geometric description of the following systems of equations? 4. 6x 9y + 6z = 3 10x 15y + 10z = 5 12x 18y + 12z = 6 x + 2y + 8z = 1 x + 3y + 10z = 0 4x + 8y + 28z = 3 5 x + 3 y z = 3 4x + 2y + z = 2 11x 5y 5z = 11 5 x + 3 y z = 3 4x + 2y + z = 2 11x 5y 5z = 8 Three identical planes Three planes intersecting at a point Three planes intersecting in a line Three planes with no common intersection 2 3 x y + z = 5 4x 2y + z = 5 13x 7y + 3z = 22 5x + 15y + 21z = 0 4x 13y 17z = 8 2x + 6y + 8z = 0 10x + 2y + 2z = 6 25x + 5y + 5z = 15 30x 6y 6z = 18 3 x y + z = 5? 4. 4x 2y + z = 5 13x 7y + 3z = 25 Unique Solution 11. (1 pt) Library/Rochester/setAlgebra35SystemMatrices- /solve RREF 2.pg Given the augmented matrix below, solve the associated system of equations. For your variables, use x1, x2, x3, x4, x5, x6, x7, and x The solution (,,,,,, ) -9--5*(x2)-1*(x3)--5*(x4)-0*(0-1*(-5-1*(9--6*(x8))--6*(x8)) x2 x3 x4 0-1*(-5-1*(9--6*(x8))--6*(x8))-1*(9--6*(x8))--6*(x8) -5-1*(9--6*(x8))--6*(x8) 9--6*(x8) x8 12. (1 pt) Library/TCNJ/TCNJ RowReduction/problem10.pg If the following system has infinitely many solutions, 7x 5y 4z = 5 9x + 2y 2z = 7 11 x y + h z = k then k =, h = 19-8
3 13. (1 pt) Library/ma112DB/set11/sw pg Given the system of equations x + y + z = 2, y 3z = 4, 2x + y + 5z = 1, (a) determine whether the system inconstent or dependent; Your answer (input inconstent or dependent) (b) if your answer dependent, find the complete solution. Write x and y as functions of z. x = y = inconstent 14. (1 pt) Library/TCNJ/TCNJ RowReduction/problem5.pg Suppose that the following 16. (1 pt) Library/Utah/College Algebra/set11 Systems of Equations and Inequalitie /1050s11p4.pg r + s + t + u = 4 r + 2s + 3t + 4u = 13 r s + 2t u = 15 r + 2s 3t + 2u = (1 pt) Library/Utah/College Algebra/set11 Systems of Equations and Inequalitie /1050s11p5.pg 6x + 8y = 2 21x + 28y = k 12x + 16y = 4 a constent system. Then k = (1 pt) Library/Utah/College Algebra/set11 Systems of Equations and Inequalities- 5 /1050s11p3.pg The principle that you process the coefficient matrix only once so important that we need to practice some more. Th and the next two problems all have the same coefficient matrix. You want to process it just once, unless you enjoy retracing your steps. r + s + t + u = 1 r + 2s + 3t + 4u = 11 r s + 2t u = 1 r + 2s 3t + 2u = (1 pt) Library/WHFreeman/Holt linear algebra/chaps 1-4- /holt pg Determine which of the points (2,4), (5,5), and ( 3,3) lie on both the lines x 1 + 3x 2 = 10 and x 1 + 5x 2 = 18. r + s + t + u = 14 r + 2s + 3t + 4u = 35 r s + 2t u = 1 r + 2s 3t + 2u = (2,4) 19. (1 pt) Library/FortLew/Algebra/5-6-Linear-systems/MCH Linear-systems.pg Find the point of intersection of the lines in the figure, given that line A, in red, has equation y = x + 3 and line B, in blue, has equation 2x + 3y = 12. x = y =
4 22. (1 pt) Library/CollegeOfIdaho/setAlgebra SystemOfLinearEq- /31IntAlg 03 LinearSystem.pg (Click on graph to enlarge) -3 / / -5 The graphs of two linear equations are shown above. the solution. None Find 20. (1 pt) Library/Rochester/setAlgebra35SystemMatrices- /solve RREF.pg Given the augmented matrix below, solve the associated system of equations. For your variables, use x1, x2, x3, x4, x5, and x (1 pt) Library/WHFreeman/Holt linear algebra/chaps 1-4- /holt pg Find the values of the coefficients a, b and c so that the conditions a = b = The solution (,,,,, ) c = -1--2*(x2)--4*(-3--3*(x4)-4*(x5)--3*(-6))-0*(x4)-3*(x5)-5*(-6) 4 x *(x4)-4*(x5)--3*(-6) -3 x4 x5 21. (1 pt) local/library/ui/holt pg Determine which of the points ( 1, 1,0), ( 5,1, 1), and (2, 5,2) lie in the plane x 1 3x 2 5x 3 = 2. (-1,-1,0) 4 f (0) = 6, f (0) = 15, and f (0) = 3 hold for the function f (x) = ae x + be 2x + ce 3x. 24. (1 pt) Library/WHFreeman/Holt linear algebra/chaps 1-4- /holt pg When using partial fractions to find antiderivatives in calculus we decompose complicated rational expressions into the sum of simpler expressions that can be integrated individually. The required decomposition 30 x(x 2 + 5) = A Bx +C + x x Find the values of the msing constants. A = B = C =
5 6 0 A system of equations can have exactly 1 solution. A system of linear equations can have exactly 1 solution. A system of linear equations has no solution if and only if there a pivot column in the echelon form of its augmented matrix. A system of linear equations has an infinite number of solutions if and only if its associated augmented matrix has a column corresponding to a free variable. If a system of linear equations has an infinite number of solutions, then its associated augmented matrix has a column corresponding to a free variable. B B 26. (1 pt) Library/WHFreeman/Holt linear algebra/chaps 1-4- /2.1.7.pg Express the following vector equation as a system of linear equations. [ ] [ ] [ ] x 1 + x 3 2 = 6 9 (Keep the equations in order.) x 1 + x 2 =. x 1 + x 2 = Generated by c WeBWorK, Mathematical Association of America 5
MATH 152 Exam 1-Solutions 135 pts. Write your answers on separate paper. You do not need to copy the questions. Show your work!!!
MATH Exam -Solutions pts Write your answers on separate paper. You do not need to copy the questions. Show your work!!!. ( pts) Find the reduced row echelon form of the matrix Solution : 4 4 6 4 4 R R
Row Reduction and Echelon Forms
Row Reduction and Echelon Forms 1 / 29 Key Concepts row echelon form, reduced row echelon form pivot position, pivot, pivot column basic variable, free variable general solution, parametric solution existence
Chapter 7 Linear Systems
Chapter 7 Linear Systems Section 1 Section 2 Section 3 Solving Systems of Linear Equations Systems of Linear Equations in Two Variables Multivariable Linear Systems Vocabulary Systems of equations Substitution
CHAPTER 1 Systems of Linear Equations
CHAPTER Systems of Linear Equations Section. Introduction to Systems of Linear Equations. Because the equation is in the form a x a y b, it is linear in the variables x and y. 0. Because the equation cannot
ft-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
Solutions of Linear system, vector and matrix equation
Goals: Solutions of Linear system, vector and matrix equation Solutions of linear system. Vectors, vector equation. Matrix equation. Math 112, Week 2 Suggested Textbook Readings: Sections 1.3, 1.4, 1.5
Chapter Practice Test Name: Period: Date:
Name: Period: Date: 1. Draw the graph of the following system: 3 x+ 5 y+ 13 = 0 29 x 11 y 7 = 0 3 13 y = x 3x+ 5y+ 13= 0 5 5 29x 11y 7 = 0 29 7 y = x 11 11 Practice Test Page 1 2. Determine the ordered
MATH 2050 Assignment 6 Fall 2018 Due: Thursday, November 1. x + y + 2z = 2 x + y + z = c 4x + 2z = 2
MATH 5 Assignment 6 Fall 8 Due: Thursday, November [5]. For what value of c does have a solution? Is it unique? x + y + z = x + y + z = c 4x + z = Writing the system as an augmented matrix, we have c R
Pre-Calculus I. For example, the system. x y 2 z. may be represented by the augmented matrix
Pre-Calculus I 8.1 Matrix Solutions to Linear Systems A matrix is a rectangular array of elements. o An array is a systematic arrangement of numbers or symbols in rows and columns. Matrices (the plural
MATH 2331 Linear Algebra. Section 1.1 Systems of Linear Equations. Finding the solution to a set of two equations in two variables: Example 1: Solve:
MATH 2331 Linear Algebra Section 1.1 Systems of Linear Equations Finding the solution to a set of two equations in two variables: Example 1: Solve: x x = 3 1 2 2x + 4x = 12 1 2 Geometric meaning: Do these
5x 2 = 10. x 1 + 7(2) = 4. x 1 3x 2 = 4. 3x 1 + 9x 2 = 8
1 To solve the system x 1 + x 2 = 4 2x 1 9x 2 = 2 we find an (easier to solve) equivalent system as follows: Replace equation 2 with (2 times equation 1 + equation 2): x 1 + x 2 = 4 Solve equation 2 for
Solutions to Homework 5 - Math 3410
Solutions to Homework 5 - Math 34 (Page 57: # 489) Determine whether the following vectors in R 4 are linearly dependent or independent: (a) (, 2, 3, ), (3, 7,, 2), (, 3, 7, 4) Solution From x(, 2, 3,
9.1 - Systems of Linear Equations: Two Variables
9.1 - Systems of Linear Equations: Two Variables Recall that a system of equations consists of two or more equations each with two or more variables. A solution to a system in two variables is an ordered
Linear Algebra I Lecture 10
Linear Algebra I Lecture 10 Xi Chen 1 1 University of Alberta January 30, 2019 Outline 1 Gauss-Jordan Algorithm ] Let A = [a ij m n be an m n matrix. To reduce A to a reduced row echelon form using elementary
Section 1.1 System of Linear Equations. Dr. Abdulla Eid. College of Science. MATHS 211: Linear Algebra
Section 1.1 System of Linear Equations College of Science MATHS 211: Linear Algebra (University of Bahrain) Linear System 1 / 33 Goals:. 1 Define system of linear equations and their solutions. 2 To represent
if b is a linear combination of u, v, w, i.e., if we can find scalars r, s, t so that ru + sv + tw = 0.
Solutions Review # Math 7 Instructions: Use the following problems to study for Exam # which will be held Wednesday Sept For a set of nonzero vectors u v w} in R n use words and/or math expressions to
Linear Algebra Practice Problems
Math 7, Professor Ramras Linear Algebra Practice Problems () Consider the following system of linear equations in the variables x, y, and z, in which the constants a and b are real numbers. x y + z = a
Matrix Factorization Reading: Lay 2.5
Matrix Factorization Reading: Lay 2.5 October, 20 You have seen that if we know the inverse A of a matrix A, we can easily solve the equation Ax = b. Solving a large number of equations Ax = b, Ax 2 =
MA 242 LINEAR ALGEBRA C1, Solutions to First Midterm Exam
MA 242 LINEAR ALGEBRA C Solutions to First Midterm Exam Prof Nikola Popovic October 2 9:am - :am Problem ( points) Determine h and k such that the solution set of x + = k 4x + h = 8 (a) is empty (b) contains
6-1 Study Guide and Intervention Multivariable Linear Systems and Row Operations
6-1 Study Guide and Intervention Multivariable Linear Systems and Row Operations Gaussian Elimination You can solve a system of linear equations using matrices. Solving a system by transforming it into
I am trying to keep these lessons as close to actual class room settings as possible.
Greetings: I am trying to keep these lessons as close to actual class room settings as possible. They do not intend to replace the text book actually they will involve the text book. An advantage of a
Math 54. Selected Solutions for Week 5
Math 54. Selected Solutions for Week 5 Section 4. (Page 94) 8. Consider the following two systems of equations: 5x + x 3x 3 = 5x + x 3x 3 = 9x + x + 5x 3 = 4x + x 6x 3 = 9 9x + x + 5x 3 = 5 4x + x 6x 3
1. Find the domain of the following functions. Write your answer using interval notation. (9 pts.)
MATH- Sample Eam Spring 7. Find the domain of the following functions. Write your answer using interval notation. (9 pts.) a. 9 f ( ) b. g ( ) 9 8 8. Write the equation of the circle in standard form given
1. Determine by inspection which of the following sets of vectors is linearly independent. 3 3.
1. Determine by inspection which of the following sets of vectors is linearly independent. (a) (d) 1, 3 4, 1 { [ [,, 1 1] 3]} (b) 1, 4 5, (c) 3 6 (e) 1, 3, 4 4 3 1 4 Solution. The answer is (a): v 1 is
Problems for M 10/12:
Math 30, Lesieutre Problem set #8 October, 05 Problems for M 0/: 4.3.3 Determine whether these vectors are a basis for R 3 by checking whether the vectors span R 3, and whether the vectors are linearly
Chapter 9: Systems of Equations and Inequalities
Chapter 9: Systems of Equations and Inequalities 9. Systems of Equations Solve the system of equations below. By this we mean, find pair(s) of numbers (x, y) (if possible) that satisfy both equations.
Assignment linearalgebrahw1 due 10/15/2012 at 02:32pm EDT
mustafa zeki Assignment linearalgebrahw1 due 10/15/2012 at 02:32pm EDT math201 1. (1 pt) Library/Rochester/setLinearAlgebra24SingularValues- /ur la 24 7.pg -1 7 Let A = 1-7 -7-1. 7 1 A singular value decomposition
Lecture 3: Gaussian Elimination, continued. Lecture 3: Gaussian Elimination, continued
Definition The process of solving a system of linear equations by converting the system to an augmented matrix is called Gaussian Elimination. The general strategy is as follows: Convert the system of
Math 3013 Solutions to Problem Set 5
Math 33 Solutions to Problem Set 5. Determine which of the following mappings are linear transformations. (a) T : R 3 R 2 : T ([x, x 2, x 3 ]) = [x + x 2, x 3x 2 ] This mapping is linear since if v = [x,
0.0.1 Section 1.2: Row Reduction and Echelon Forms Echelon form (or row echelon form): 1. All nonzero rows are above any rows of all zeros.
0.0.1 Section 1.2: Row Reduction and Echelon Forms Echelon form (or row echelon form): 1. All nonzero rows are above any rows of all zeros. 2. Each leading entry (i.e. left most nonzero entry) of a row
Math Analysis Notes Mrs. Atkinson 1
Name: Math Analysis Chapter 7 Notes Day 6: Section 7-1 Solving Systems of Equations with Two Variables; Sections 7-1: Solving Systems of Equations with Two Variables Solving Systems of equations with two
Chapter 3. Vector spaces
Chapter 3. Vector spaces Lecture notes for MA1111 P. Karageorgis pete@maths.tcd.ie 1/22 Linear combinations Suppose that v 1,v 2,...,v n and v are vectors in R m. Definition 3.1 Linear combination We say
SOLUTIONS FOR PROBLEMS 1-30
. Answer: 5 Evaluate x x + 9 for x SOLUTIONS FOR PROBLEMS - 0 When substituting x in x be sure to do the exponent before the multiplication by to get (). + 9 5 + When multiplying ( ) so that ( 7) ( ).
ft-uiowa-math2550 Assignment NOTRequiredJustHWformatOfQuizReviewForExam3part2 due 12/31/2014 at 07:10pm CST
me me ft-uiowa-math2550 Assignment NOTRequiredJustHWformatOfQuizReviewForExam3part2 due 12/31/2014 at 07:10pm CST 1. (1 pt) local/library/ui/eigentf.pg A is n n an matrices.. There are an infinite number
x 1 2x 2 +x 3 = 0 2x 2 8x 3 = 8 4x 1 +5x 2 +9x 3 = 9
Sec 2.1 Row Operations and Gaussian Elimination Consider a system of linear equations x 1 2x 2 +x 3 = 0 2x 2 8x 3 = 8 4x 1 +5x 2 +9x 3 = 9 The coefficient matrix of the system is The augmented matrix of
3.4 Elementary Matrices and Matrix Inverse
Math 220: Summer 2015 3.4 Elementary Matrices and Matrix Inverse A n n elementary matrix is a matrix which is obtained from the n n identity matrix I n n by a single elementary row operation. Elementary
3-1 Graphing and Writing Inequalities. Warm Up Lesson Presentation Lesson Quiz
3-1 Graphing and Writing Inequalities Warm Up Lesson Presentation Lesson Quiz Holt Holt Algebra Algebra 1 1 Bell Quiz 3-1 Compare. Write , or =. 2 pts 1. 3 2 2 pts 2. 6.5 6.3 1 pt for putting your
Announcements Wednesday, August 30
Announcements Wednesday, August 30 WeBWorK due on Friday at 11:59pm. The first quiz is on Friday, during recitation. It covers through Monday s material. Quizzes mostly test your understanding of the homework.
Partial Fractions. Calculus 2 Lia Vas
Calculus Lia Vas Partial Fractions rational function is a quotient of two polynomial functions The method of partial fractions is a general method for evaluating integrals of rational function The idea
Homework 1 Due: Wednesday, August 27. x + y + z = 1. x y = 3 x + y + z = c 2 2x + cz = 4
Homework 1 Due: Wednesday, August 27 1. Find all values of c for which the linear system: (a) has no solutions. (b) has exactly one solution. (c) has infinitely many solutions. (d) is consistent. x + y
Lecture 03. Math 22 Summer 2017 Section 2 June 26, 2017
Lecture 03 Math 22 Summer 2017 Section 2 June 26, 2017 Just for today (10 minutes) Review row reduction algorithm (40 minutes) 1.3 (15 minutes) Classwork Review row reduction algorithm Review row reduction
Solving Systems of Linear Equations. Classification by Number of Solutions
Solving Systems of Linear Equations Case 1: One Solution Case : No Solution Case 3: Infinite Solutions Independent System Inconsistent System Dependent System x = 4 y = Classification by Number of Solutions
Finite Mathematics Chapter 2. where a, b, c, d, h, and k are real numbers and neither a and b nor c and d are both zero.
Finite Mathematics Chapter 2 Section 2.1 Systems of Linear Equations: An Introduction Systems of Equations Recall that a system of two linear equations in two variables may be written in the general form
Announcements Wednesday, August 30
Announcements Wednesday, August 30 WeBWorK due on Friday at 11:59pm. The first quiz is on Friday, during recitation. It covers through Monday s material. Quizzes mostly test your understanding of the homework.
Assignment linearalgebrahw1 due 10/15/2012 at 02:32pm EDT
mustafa zeki Assignment linearalgebrahw1 due 10/15/2012 at 02:32pm EDT math201 1 (1 pt) Library/Rochester/setLinearAlgebra24SingularValues- /ur la 24 7pg -1 7 Let A 1-7 -7-1 7 1 A singular value decomposition
King Fahd University of Petroleum and Minerals Prep-Year Math Program Math (001) - Term 181 Recitation (1.1)
Recitation (1.1) Question 1: Find a point on the y-axis that is equidistant from the points (5, 5) and (1, 1) Question 2: Find the distance between the points P(2 x, 7 x) and Q( 2 x, 4 x) where x 0. Question
Chapter 1 Linear Equations. 1.1 Systems of Linear Equations
Chapter Linear Equations. Systems of Linear Equations A linear equation in the n variables x, x 2,..., x n is one that can be expressed in the form a x + a 2 x 2 + + a n x n = b where a, a 2,..., a n and
Midterm 1 Solutions Math Section 55 - Spring 2018 Instructor: Daren Cheng
Midterm 1 Solutions Math 20250 Section 55 - Spring 2018 Instructor: Daren Cheng #1 Do the following problems using row reduction. (a) (6 pts) Let A = 2 1 2 6 1 3 8 17 3 5 4 5 Find bases for N A and R A,
College Algebra. Systems of Equations and Inequalities with Matrices addendum to Lesson2. Dr. Francesco Strazzullo, Reinhardt University
College Algebra Systems of Equations and Inequalities with Matrices addendum to Lesson2 Dr. Francesco Strazzullo, Reinhardt University Objectives These notes concern topics covered in our textbook, at
Systems of Linear Equations in Two Variables. Break Even. Example. 240x x This is when total cost equals total revenue.
Systems of Linear Equations in Two Variables 1 Break Even This is when total cost equals total revenue C(x) = R(x) A company breaks even when the profit is zero P(x) = R(x) C(x) = 0 2 R x 565x C x 6000
MATH 3321 Sample Questions for Exam 3. 3y y, C = Perform the indicated operations, if possible: (a) AC (b) AB (c) B + AC (d) CBA
MATH 33 Sample Questions for Exam 3. Find x and y so that x 4 3 5x 3y + y = 5 5. x = 3/7, y = 49/7. Let A = 3 4, B = 3 5, C = 3 Perform the indicated operations, if possible: a AC b AB c B + AC d CBA AB
Math 1050 Exam 2 Name. D) no vertical asymptotes
Math 050 Exam 2 Name Give the equation of the specified asymptote(s). 3x - 7 ) Vertical asymptote(s): f(x) = x2-5x - 4 A) x = -7, x = 2 B) x = 7, x = 7, x = -2 3 C)x = 7, x = -2 D) no vertical asymptotes
1. (7pts) Find the points of intersection, if any, of the following planes. 3x + 9y + 6z = 3 2x 6y 4z = 2 x + 3y + 2z = 1
Math 125 Exam 1 Version 1 February 20, 2006 1. (a) (7pts) Find the points of intersection, if any, of the following planes. Solution: augmented R 1 R 3 3x + 9y + 6z = 3 2x 6y 4z = 2 x + 3y + 2z = 1 3 9
Systems of Equations Homework Solutions
Systems of Equations Homework Solutions Olena Bormashenko October 5, 2011 Find all solutions to the following systems of equations by writing the system as an augmented matrix and row-reducing it until
MATH 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
Chapter 1. Vectors, Matrices, and Linear Spaces
1.4 Solving Systems of Linear Equations 1 Chapter 1. Vectors, Matrices, and Linear Spaces 1.4. Solving Systems of Linear Equations Note. We give an algorithm for solving a system of linear equations (called
MATH 225 Summer 2005 Linear Algebra II Solutions to Assignment 1 Due: Wednesday July 13, 2005
MATH 225 Summer 25 Linear Algebra II Solutions to Assignment 1 Due: Wednesday July 13, 25 Department of Mathematical and Statistical Sciences University of Alberta Question 1. [p 224. #2] The set of all
5) homogeneous and nonhomogeneous systems 5a) The homogeneous matrix equation, A x = 0 is always consistent.
5) homogeneous and nonhomogeneous systems 5a) The homogeneous matrix equation, A x is always consistent. 5b) If A x b is also consistent, then the solution set to A x b is a translation of the solution
Matrix equation Ax = b
Fall 2017 Matrix equation Ax = b Authors: Alexander Knop Institute: UC San Diego Previously On Math 18 DEFINITION If v 1,..., v l R n, then a set of all linear combinations of them is called Span {v 1,...,
Math 240, 4.3 Linear Independence; Bases A. DeCelles. 1. definitions of linear independence, linear dependence, dependence relation, basis
Math 24 4.3 Linear Independence; Bases A. DeCelles Overview Main ideas:. definitions of linear independence linear dependence dependence relation basis 2. characterization of linearly dependent set using
MAT 1302B Mathematical Methods II
MAT 1302B Mathematical Methods II Alistair Savage Mathematics and Statistics University of Ottawa Winter 2015 Lecture 3 Alistair Savage (uottawa) MAT 1302B Mathematical Methods II Winter 2015 Lecture 3
Name: Section Registered In:
Name: Section Registered In: Math 125 Exam 1 Version 1 February 21, 2006 60 points possible 1. (a) (3pts) Define what it means for a linear system to be inconsistent. Solution: A linear system is inconsistent
And, even if it is square, we may not be able to use EROs to get to the identity matrix. Consider
.2. Echelon Form and Reduced Row Echelon Form In this section, we address what we are trying to achieve by doing EROs. We are trying to turn any linear system into a simpler one. But what does simpler
Solutions to Homework 2
Solutions to Homewor Due Tuesday, July 6,. Chapter. Problem solution. If the series for ln+z and ln z both converge, +z then we can find the series for ln z by term-by-term subtraction of the two series:
Math 301 Test I. M. Randall Holmes. September 8, 2008
Math 0 Test I M. Randall Holmes September 8, 008 This exam will begin at 9:40 am and end at 0:5 am. You may use your writing instrument, a calculator, and your test paper; books, notes and neighbors to
MATH 54 - WORKSHEET 1 MONDAY 6/22
MATH 54 - WORKSHEET 1 MONDAY 6/22 Row Operations: (1 (Replacement Add a multiple of one row to another row. (2 (Interchange Swap two rows. (3 (Scaling Multiply an entire row by a nonzero constant. A matrix
Solutions to Math 51 First Exam October 13, 2015
Solutions to Math First Exam October 3, 2. (8 points) (a) Find an equation for the plane in R 3 that contains both the x-axis and the point (,, 2). The equation should be of the form ax + by + cz = d.
Check 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
Math 314H EXAM I. 1. (28 points) The row reduced echelon form of the augmented matrix for the system. is the matrix
Math 34H EXAM I Do all of the problems below. Point values for each of the problems are adjacent to the problem number. Calculators may be used to check your answer but not to arrive at your answer. That
Assignment busshw1 due 10/15/2012 at 01:04pm EDT
Administrator Assignment busshw1 due 10/15/2012 at 01:04pm EDT math111 1. (1 pt) Library/Rochester/setVectors0Introduction/ur vc 0 2.pg If the distance from the town of Bree to Weathertop is 6 miles on
Math Models of OR: Some Definitions
Math Models of OR: Some Definitions John E. Mitchell Department of Mathematical Sciences RPI, Troy, NY 12180 USA September 2018 Mitchell Some Definitions 1 / 20 Active constraints Outline 1 Active constraints
Cathedral Catholic High School Course Catalog
Cathedral Catholic High School Course Catalog Course Title: Pre-Calculus Course Description: This course is designed to prepare students to begin their college studies in introductory Calculus. Students
Math 3C Lecture 25. John Douglas Moore
Math 3C Lecture 25 John Douglas Moore June 1, 2009 Let V be a vector space. A basis for V is a collection of vectors {v 1,..., v k } such that 1. V = Span{v 1,..., v k }, and 2. {v 1,..., v k } are linearly
Connor Ahlbach Math 308 Notes
Connor Ahlbach Math 308 Notes. Echelon Form and educed ow Echelon Form In this section, we address what we are trying to acheive by doing EOs. We are trying to turn a complicated linear system into s simpler
Recall, we solved the system below in a previous section. Here, we learn another method. x + 4y = 14 5x + 3y = 2
We will learn how to use a matrix to solve a system of equations. College algebra Class notes Matrices and Systems of Equations (section 6.) Recall, we solved the system below in a previous section. Here,
Math Studio College Algebra
Math 100 - Studio College Algebra Rekha Natarajan Kansas State University November 19, 2014 Systems of Equations Systems of Equations A system of equations consists of Systems of Equations A system of
Lecture 2 Systems of Linear Equations and Matrices, Continued
Lecture 2 Systems of Linear Equations and Matrices, Continued Math 19620 Outline of Lecture Algorithm for putting a matrix in row reduced echelon form - i.e. Gauss-Jordan Elimination Number of Solutions
Math 220: Summer Midterm 1 Questions
Math 220: Summer 2015 Midterm 1 Questions MOST questions will either look a lot like a Homework questions This lists draws your attention to some important types of HW questions. SOME questions will have
1 Linear systems, existence, uniqueness
Jor-el Briones / Math 2F, 25 Summer Session, Practice Midterm Page of 9 Linear systems, existence, uniqueness For each part, construct an augmented matrix for a linear system with the given properties,
If A is a 4 6 matrix and B is a 6 3 matrix then the dimension of AB is A. 4 6 B. 6 6 C. 4 3 D. 3 4 E. Undefined
Question 1 If A is a 4 6 matrix and B is a 6 3 matrix then the dimension of AB is A. 4 6 B. 6 6 C. 4 3 D. 3 4 E. Undefined Quang T. Bach Math 18 October 18, 2017 1 / 17 Question 2 1 2 Let A = 3 4 1 2 3
b for the linear system x 1 + x 2 + a 2 x 3 = a x 1 + x 3 = 3 x 1 + x 2 + 9x 3 = 3 ] 1 1 a 2 a
![b for the linear system x 1 + x 2 + a 2 x 3 = a x 1 + x 3 = 3 x 1 + x 2 + 9x 3 = 3 ] 1 1 a 2 a](/thumbs/71/65559666.jpg "b for the linear system x 1 + x 2 + a 2 x 3 = a x 1 + x 3 = 3 x 1 + x 2 + 9x 3 = 3 ] 1 1 a 2 a")
Practice Exercises for Exam Exam will be on Monday, September 8, 7. The syllabus for Exam consists of Sections One.I, One.III, Two.I, and Two.II. You should know the main definitions, results and computational
Miller Objectives Alignment Math
Miller Objectives Alignment Math 1050 1 College Algebra Course Objectives Spring Semester 2016 1. Use algebraic methods to solve a variety of problems involving exponential, logarithmic, polynomial, and
Multiple Choice Questions
Multiple Choice Questions There is no penalty for guessing. Three points per question, so a total of 48 points for this section.. What is the complete relationship between homogeneous linear systems of
Midterm 1 Review. Written by Victoria Kala SH 6432u Office Hours: R 12:30 1:30 pm Last updated 10/10/2015
Midterm 1 Review Written by Victoria Kala vtkala@math.ucsb.edu SH 6432u Office Hours: R 12:30 1:30 pm Last updated 10/10/2015 Summary This Midterm Review contains notes on sections 1.1 1.5 and 1.7 in your
Chapter 1: Systems of Linear Equations and Matrices
: Systems of Linear Equations and Matrices Multiple Choice Questions. Which of the following equations is linear? (A) x + 3x 3 + 4x 4 3 = 5 (B) 3x x + x 3 = 5 (C) 5x + 5 x x 3 = x + cos (x ) + 4x 3 = 7.
Homework 1.1 and 1.2 WITH SOLUTIONS
Math 220 Linear Algebra (Spring 2018) Homework 1.1 and 1.2 WITH SOLUTIONS Due Thursday January 25 These will be graded in detail and will count as two (TA graded) homeworks. Be sure to start each of these
Sample Final Exam. Math S o l u t i o n s. 1. Three points are given: A = ( 2, 2), B = (2, 4), C = ( 4, 0)
Math 0031 Sample Final Exam S o l u t i o n s 1. Three points are given: A = ( 2, 2), B = (2, 4), C = ( 4, 0) (a) (5 points) Find the midpoint D of the segment with endpoints B and C. ( 2 + ( 4) D =, 4
Math 2331 Linear Algebra
1.2 Echelon Forms Math 2331 Linear Algebra 1.2 Row Reduction and Echelon Forms Shang-Huan Chiu Department of Mathematics, University of Houston schiu@math.uh.edu math.uh.edu/ schiu/ January 22, 2018 Shang-Huan
MODEL ANSWERS TO THE FIRST QUIZ. 1. (18pts) (i) Give the definition of a m n matrix. A m n matrix with entries in a field F is a function
MODEL ANSWERS TO THE FIRST QUIZ 1. (18pts) (i) Give the definition of a m n matrix. A m n matrix with entries in a field F is a function A: I J F, where I is the set of integers between 1 and m and J is
Section 8.3 Partial Fraction Decomposition
Section 8.6 Lecture Notes Page 1 of 10 Section 8.3 Partial Fraction Decomposition Partial fraction decomposition involves decomposing a rational function, or reversing the process of combining two or more
Linear Independence x
Linear Independence A consistent system of linear equations with matrix equation Ax = b, where A is an m n matrix, has a solution set whose graph in R n is a linear object, that is, has one of only n +
DM559 Linear and Integer Programming. Lecture 2 Systems of Linear Equations. Marco Chiarandini
DM559 Linear and Integer Programming Lecture Marco Chiarandini Department of Mathematics & Computer Science University of Southern Denmark Outline 1. Outline 1. 3 A Motivating Example You are organizing
Partial Fraction Decomposition Honors Precalculus Mr. Velazquez Rm. 254
Partial Fraction Decomposition Honors Precalculus Mr. Velazquez Rm. 254 Adding and Subtracting Rational Expressions Recall that we can use multiplication and common denominators to write a sum or difference
Math 250B Midterm II Review Session Spring 2019 SOLUTIONS
Math 250B Midterm II Review Session Spring 2019 SOLUTIONS [ Problem #1: Find a spanning set for nullspace 1 2 0 2 3 4 8 0 8 12 1 2 0 2 3 SOLUTION: The row-reduced form of this matrix is Setting 0 0 0 0
Linear Algebra Final Exam Study Guide Solutions Fall 2012
. Let A = Given that v = 7 7 67 5 75 78 Linear Algebra Final Exam Study Guide Solutions Fall 5 explain why it is not possible to diagonalize A. is an eigenvector for A and λ = is an eigenvalue for A diagonalize
WeBWorK demonstration assignment
WeBWorK demonstration assignment The main purpose of this WeBWorK set is to familiarize yourself with WeBWorK. Here are some hints on how to use WeBWorK effectively: After first logging into WeBWorK change
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
est Review-Linear Algebra Name MULIPLE CHOICE Choose the one alternative that best completes the statement or answers the question Solve the system of equations ) 7x + 7 + x + + 9x + + 9 9 (-,, ) (, -,
Additional Problems for Midterm 1 Review
Additional Problems for Midterm Review About This Review Set As stated in the syllabus, a goal of this course is to prepare students for more advanced courses that have this course as a pre-requisite.
Matrices. A matrix is a method of writing a set of numbers using rows and columns. Cells in a matrix can be referenced in the form.
Matrices A matrix is a method of writing a set of numbers using rows and columns. 1 2 3 4 3 2 1 5 7 2 5 4 2 0 5 10 12 8 4 9 25 30 1 1 Reading Information from a Matrix Cells in a matrix can be referenced
FINAL (CHAPTERS 7-9) MATH 141 SPRING 2018 KUNIYUKI 250 POINTS TOTAL
Math 141 Name: FINAL (CHAPTERS 7-9) MATH 141 SPRING 2018 KUNIYUKI 250 POINTS TOTAL Show all work, simplify as appropriate, and use good form and procedure (as in class). Box in your final answers! No notes