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 of A is as follows: -1 1 1-1 -5 0 A 1-1 1-1 0-5 06 08 1 1 1 1 0 0 08-06 -1-1 1 1 0 0 Find the least-squares solution of the linear system -1 A b, where b -1-4 -4 x1, x2 2 (1 pt) Library/Rochester/setLinearAlgebra3Matrices/ur la 3 33pg Find a non-zero, two-by-two matrix such that: -6-9 0 0 24 36 0 0 3 (1 pt) Library/Rochester/setLinearAlgebra3Matrices/ur Ch1 3 4pg 5x + 7y 8z 3 3x + 8y 5z 3 4x + 1y 5z 7 Write the above system of equations in matrix form: x y z 4 (1 pt) Library/Rochester/setLinearAlgebra3Matrices/ur la 3 25pg x 5 If A, determine the values of x and y for which y -6 A 2 A, 5 (1 pt) Library/Rochester/setLinearAlgebra3Matrices/ur la 3 15pg Find a and b such that -23-21 a 3 +b 3-25 a b 3 5 6 (1 pt) Library/Rochester/setLinearAlgebra3Matrices/ur la 3 34pg Find a non-zero, two-by-two matrix such that: 0 0 A 2 A 0 0 7 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 16pg x +y 6 5x 3y 6 11x 5y 18 8 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 12pg Determine the value of k for which the system has no solutions k x +y+5z 1 x +2y 3z 1 6x+13y+kz 9 9 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 3pg using substitution x 3y 4 3x 8y 5 10 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 4pg using substitution 8x+5y 43 7x+4y 38 11 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 5pg using elimination z 2x+3y+5z 35 3x+2y 4z 19 6x 5y+2z 25 1

12 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 17pg x 1 x 3 x 4 x 1 +2x 3 +2x 4 26 4x 3 3x 4 38 2x 1 3 +18x 3 +13x 4 180 +4x 3 +7x 4 54 13 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 15pg x 1 +3x 3 6 4x 1 3 +5x 3 3 3x 1 +12x 3 45 x 1 x 3 + s 14 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 14pg x1 + +4x 3 8 x 1 x 3 3x 1 +2 3x 3 6 + s 15 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 4bpg using matrices (row operations) 8x+5y 69 7x 5y 51 16 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 6pg For each system, determine whether it has a unique solution (in this case, find the solution), infinitely many solutions, or no solutions 1 2x+3y 20 6x+9y 59 A Unique solution: 59, 20 B No solutions C Unique solution: 0, 0 D Infinitely many solutions E Unique solution: 20, 59 F None of the above 2 2 2x+2y10 6x+6y30 A Unique solution: 0, 0 B Infinitely many solutions C Unique solution: 10, 30 D No solutions E Unique solution: 5, 0 F None of the above 3 9x+7y0 6x+3y0 A Unique solution: 2, 3 B No solutions C Unique solution: 3, 9 D Infinitely many solutions E Unique solution: 0, 0 F None of the above 4 5x+4y 0 6x 7y11 A No solutions B Unique solution: 4, 5 C Unique solution: 5, 4 D Unique solution: 0, 0 E Infinitely many solutions F None of the above 17 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 4apg using elimination 2x 7y 18 9x+8y 13 18 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 1pg Perform one step of row reduction, in order to calculate the values for x and y by back substitution Then calculate the values for x and for y Also calculate the determinant of the original matrix You can let webwork do much of the calculation for you if you want (eg enter 45-(56/76)(-3) instead of calculating the value out) You can also use the preview feature in order to make sure that you have used the correct syntax in entering the answer Note since the determinant is unchanged by row reduction it will be easier to calculate the determinant of the row reduced matrix 2 20 x 10-8 y 2 20 0 x y -2 4-2

det 19 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 21pg x 1 y 1 y 2 The dot product of two vectors x n and y n in R n is defined by x x 1 y 1 + y 2 + + x n y n The vectors x and y are called perpendicular if x 0 Then any vector in R 3 perpendicular to -2-2 can be written -3 in the form s + t 20 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 4cpg by using Cramer s Rule 4x+7y 11 7x+2y 5 21 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 22pg The reduced row-echelon forms of the augmented matrices of four systems are given below How many solutions does each system have? 1 1 0 1 0 0 1 11 0 0 0 0 1 A Infinitely many solutions B No solutions C Unique solution D None of the above 1 0 0 3 2 0 0 1-7 A Unique solution B No solutions C Infinitely many solutions D None of the above 0 1 0-13 3 0 0 1 2 A Infinitely many solutions B No solutions C Unique solution D None of the above 1 0 19 4 0 1-5 A No solutions B Infinitely many solutions C Unique solution D None of the above 3 22 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 23pg Write the system in matrix form 2y 3z 2 7x+11 10 3x 4y 6z 9 x y z 23 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 20pg x 1 x 3 x 4 x 5 x 6 + u x 1 4 +2x 3 4x 5 +5x 6 4 x 4 5x 5 +5x 6 5 x 1 4 6x 5 9x 6 4 + s + 24 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 7pg Write the augmented matrix of the system 48x +3z3 8x 2y z4 47x+783 25 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 5apg using matrices (row operations) z 2x 4y+5z 13 3x+2y+4z 10 2x 3y 2z 29 t

26 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 10pg Solve the equation x y z 8x + 7y + 5z 10 + s + t 27 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 19pg x 1 x 3 x 4 4x 1 5 +2x 3 +4x 4 0 x 1 + +3x 3 +3x 4 2 3x 1 4 +5x 3 +7x 4 2 3x 1 3 9x 3 9x 4 6 + s + t 28 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 9pg Determine the value of h such that the matrix is the augmented matrix of a linear system with infinitely many solutions h 3 5 9 h 29 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 11pg 2 6 4x+5ya 5x 6yb 30 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 13pg 2x1 + 3 x1 6x 1 3 9 + s 31 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 8pg Determine the value of h such that the matrix is the augmented matrix of a consistent linear system h 3 2 9 6 h 8 32 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 18pg x 1 + 2 +x 3 5 x 3 +x 4 2 x 1 +x 4 5 x 1 x 3 x 4 + s 33 (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 2pg Perform one step of row reduction, in order to calculate the values for x and y by back substitution Then calculate the values for x and for y Also calculate the determinant of the original matrix You can let webwork do much of the calculation for you if you want (eg enter 45-(56/76)(-3) instead of calculating the value out) You can also use the preview feature in order to make sure that you have used the correct syntax in entering the answer This problem has rather difficult complex calculations Note since the determinant is unchanged by row reduction it will be easier to calculate the determinant of the row reduced matrix 1+2i -2-4i x -2+2i 4-2i y 1+2i -2-4i -1-7i 4-2i x y -1-7i 0 det 34 (1 pt) Library/Rochester/setLinearAlgebra2SystemsApplications- /ur la 2 2pg Find the quadratic polynomial whose graph goes through the points ( 2,6), (0,4), and (2,18) f (x) + x+ 35 (1 pt) Library/Rochester/setLinearAlgebra2SystemsApplications- /ur la 2 7pg Consider a two-commodity market When the unit prices of the products are P 1 and P 2, the quantities demanded, D 1 and D 2, and the quantities supplied, S 1 and S 2, are given by D 1 55 3P 1 + P 2 D 2 163+ P 1 3P 2 S 1 28+2P 1 S 2 22 +2P 2 (a) What is the relationship between the two commodities? Do they compete, as do Volvos and BMWs, or do they complement one another, as do shirts and ties? (type in compete or complement ) 4

(b) Find the equilibrium prices (ie the prices for which supply equals demand), for both products P 1 P 2 36 (1 pt) Library/Rochester/setLinearAlgebra2SystemsApplications- /ur la 2 6pg In a grid of wires, the temperature at exterior mesh poins is maintained at constant values as shown in the figure When the grid is in thermal equilibrium, the temperature at each interior mesh point is the average of the temperatures at the four adjacent points For instance, T 1 T 2 + T 3 + 20 140 4 Find the temperatures T 1, T 2, T 3, T 4, when the grid is in thermal equilibrium Nutrient Food 1 Food 2 Food 3 Total Required (mg) Vitamin C 30 60 45 390 Calcium 10 30 35 220 Magnesium 30 80 55 480 Write the augmented matrix for this problem What quantity (in units) of Food 1 is necesary to meet the dietary requirements? What quantity (in units) of Food 2 is necesary to meet the dietary requirements? What quantity (in units) of Food 3 is necesary to meet the dietary requirements? T 1 T 2 T 3 T 4 37 (1 pt) Library/Rochester/setLinearAlgebra2SystemsApplications- /ur la 2 1pg Tonya and Steve are sister and brother Tonya has twice as many brothers as sisters, and Steve has as many brothers as sisters How many girls and boys are there in this family? Answer: girls and boys 38 (1 pt) Library/Rochester/setLinearAlgebra2SystemsApplications- /ur la 2 8pg A dietitian is planning a meal that supplies certain quantities of vitamin C, calcium, and magnesium Three foods will be used, their quantities measured in milligrams The nutrients supplied by one unit of each food and the dietary requirements are given in the table below 5 39 (1 pt) Library/Rochester/setLinearAlgebra2SystemsApplications- /ur la 2 5pg Consider the chemical reaction an 2 H 4 + bn 2 O 4 cn 2 + dh 2 O, where a, b, c, and d are unknown positive integers The reaction mush be balanced; that is, the number of atoms of each element must be the same before and after the reaction For example, because the number of oxygen atoms must remain the same, 4b d While there are many possible choices for a, b, c, and d that balance the reaction, it is customary to use the smallest possible integers Balance this reaction a b c d 40 (1 pt) Library/Rochester/setLinearAlgebra2SystemsApplications- /ur la 2 3pg Find the polynomial of degree 4 whose graph goes through the points ( 2, 54), ( 1, 3), (0,2), (2, 6), and (3, 139) f (x) x 4 + x 3 + + x+ 41 (1 pt) Library/Rochester/setLinearAlgebra2SystemsApplications- /ur la 2 4pg Find the cubic polynomial f (x) such that f (1) 3, f (1) 6, f (1) 16, and f (1) 12 f (x) x 3 + + x+ 42 (1 pt) Library/Rochester/setAlgebra34Matrices/sw7 4 5pg Given the matrices 4 3 3 2 2-3 B, C, -5 2-4 -2 1-1 find 3B + 2C Write 3B + 2C as a11 a 3B + 2C 12 a 13 a 21 a 22 a 23

Input your answer below: a 11 a 12 a 13 a 21 a 22 a 23 43 (1 pt) Library/Rochester/setAlgebra34Matrices/sw7 4 1pg Given the matrices -2 1-4 1-4 -2 B, C, -1 4 0 1 3-5 find B +C Write B +C as a11 a B +C 12 a 13 a 21 a 22 a 23 Input your answer below: a 11 a 12 a 13 a 21 a 22 a 23 44 (1 pt) Library/Rochester/setAlgebra34Matrices/scalarmult3pg If A 2 3 0-3 -2-4 4 0-3 and B 1 2 0-4 0-3 2 0 4 Then 2A + B and A T 45 (1 pt) Library/Rochester/setAlgebra34Matrices/sw7 4 3pg Given the matrices -5-4 -1 1 0 2 B, C, -2 2-2 -2 2 2 find C B Write C B as a11 a C B 12 a 13 a 21 a 22 a 23 Input your answer below: a 11 a 12 a 13 a 21 a 22 a 23 46 (1 pt) Library/Rochester/setAlgebra34Matrices/scalarmult3apg If A -2 0 1-2 1-1 0-4 -4 and B -1 1 1 4-3 1-4 4 4 6 Then 2A 2B and 4A T 47 (1 pt) Library/Rochester/setLinearAlgebra20LeastSquares- /ur la 20 4pg Find the least-squares solution x of the system 1 1 1 1-1 -1 1 1-1 1-1 1 x -2-2 -4 12 48 (1 pt) Library/Rochester/setLinearAlgebra20LeastSquares- /ur la 20 7pg Fit a trigonometric function of the form f (t) c 0 + c 1 sin(t) + c 2 cos(t) to the data points (0, 2), ( π 2,5), (π, 12), ( 3π 2, 7), using least squares c 0, c 1, c 2 49 (1 pt) Library/Rochester/setLinearAlgebra20LeastSquares- /ur la 20 6pg Fit a quadratic function of the form f (t) c 0 + c 1 t + c 2 t 2 to the data points (0, 7), (1, 13), (2, 11), (3, 21), using least squares c 0, c 1, c 2 50 (1 pt) Library/Rochester/setLinearAlgebra20LeastSquares- /ur la 20 3pg Find the least-squares solution x of the system 6-5 22-13 -2 1 x 51 (1 pt) Library/Rochester/setLinearAlgebra20LeastSquares- /ur la 20 9pg The table below lists the height h (in cm), the age a (in years), the gender g (1 Male, 0 Female ), and the weight w (in kg) of some college students Height Age Gender Weight 180 20 1 83 163 20 0 58 168 21 0 63 155 22 0 51 174 20 1 78

We wish to fit a linear function of the form w(t) c 0 + c 1 h + c 2 a + c 3 g which predicts the weight from the rest of the data Find the best approximation of this function, using least squares c 0, c 1, c 2, c 3 52 (1 pt) Library/Rochester/setLinearAlgebra20LeastSquares- /ur la 20 8pg Let S(t) be the number of daylight hours on the tth day of the year in Manley Hot Springs We are given the following data for S(t): Day t S(t) January 8 8 5 March 16 75 12 May 23 143 19 July 17 198 20 We wish to fit a trigonometric function of the form ( ) ( ) 2π 2π f (t) a + bsin 365 t + ccos 365 t to these data Find the best approximation of this form, using least squares a, b, c 53 (1 pt) Library/Rochester/setLinearAlgebra20LeastSquares- /ur la 20 10pg During the summer months Terry makes and sells necklaces on the beach Terry notices that if he lowers the price, he can sell more necklaces, and if he raises the price than he sells fewer necklaces The table below shows how the number n of necklaces sold in one day depends on the price p (in dollars) Price Number of necklaces sold 7 31 11 23 15 14 (a) Find a linear function of the form n c 0 + c 1 p that best fits these data, using least squares c 0, c 1 (b) Find the revenue (number of items sold times the price of each item) as a function of price p R (c) If the material for each necklace costs Terry 5 dollars, find the profit (revenue minus cost of the material) as a function of price p P 7 (d) Finally, find the price that will maximize the profit p 54 (1 pt) Library/Rochester/setLinearAlgebra20LeastSquares- /ur la 20 5pg Fit a linear function of the form f (t) c 0 +c 1 t to the data points ( 9,60), (0,0), (9, 66), using least squares c 0, c 1 55 (1 pt) Library/Rochester/setLinearAlgebra20LeastSquares- /ur la 20 2pg Find the least-squares solution x of the system 1-1 -1 1 3-9 5 3-10 x 56 (1 pt) Library/Rochester/setLinearAlgebra20LeastSquares- /ur la 20 1pg Find the least-squares solution x of the system 1 0 0 1 0 0-3 -9 5 x 57 (1 pt) Library/maCalcDB/setLinearAlgebra1Systems/ur la 1 3pg using substitution x 4y3 4x 14y4 58 (1 pt) Library/maCalcDB/setLinearAlgebra1Systems/ur la 1 4pg using substitution 4x+3y 42 9x+5y 24 59 (1 pt) Library/maCalcDB/setLinearAlgebra1Systems/ur la 1 5pg using elimination z 2x 2y 5z 21 5x 2y 2z 26 5x 3y+4z 7

60 (1 pt) Library/maCalcDB/setLinearAlgebra1Systems- /ur la 1 4apg using elimination 8x+5y 41 3x 4y 26 61 (1 pt) Library/maCalcDB/setLinearAlgebra1Systems/ur la 1 7pg Write the augmented matrix of the system x 69y +9z63 18y 6z 0 91x +93z 0 65 (1 pt) Library/TCNJ/TCNJ LinearSystems/problem7pg x 4 1 2x 9 5 66 (1 pt) Library/TCNJ/TCNJ LinearSystems/problem15pg : 4x 3 a 3x 2 b 67 (1 pt) Library/TCNJ/TCNJ LinearSystems/problem1pg Determine whether the following system has no solution, an infinite number of solutions or a unique solution 62 (1 pt) Library/TCNJ/TCNJ LinearSystems/problem2pg Determine whether the following system has no solution, an infinite number of solutions or a unique solution? 3 10x + 10y 25z 0 6x 6y + 15z 0 10x + 10y 25z 0 6x 6y + 15z 1 3x 4y + 3z 1 3x + 3y + 7z 7? 3 5x +5 3 4x 2 5 11x 13 17 5x +5 3 4x 2 5 11x 13 20 20x +20 5 8x 8 2 28x +28 7 63 (1 pt) Library/TCNJ/TCNJ LinearSystems/problem18pg Determine all values of h and k for which the system 9x + 5 h 6x + k 7 has no solution k h 64 (1 pt) Library/TCNJ/TCNJ LinearSystems/problem4pg Give a geometric description of the following system of equations? 3 2x + 4y 6z 12 3x 6y + 9z 18 2x + 4y 6z 12 x + 5y 9z 1 2x + 4y 6z 12 3x 6y + 9z 16 68 (1 pt) Library/TCNJ/TCNJ LinearSystems/problem19pg The system 6x 30y 35z 0 8x + 39y + 46z 0 5x + 25y + 30z 0 has the solution,, z 69 (1 pt) Library/TCNJ/TCNJ LinearSystems/problem14pg using elimination z 2x 2y+3z 5 3x+2y+4z 18 6x 5y+4z 5 8

70 (1 pt) Library/TCNJ/TCNJ LinearSystems/problem13pg Determine the value of k for which the system x +y+5z 2 x +2y 3z 2 5x+12y+kz11 has no solutions k 71 (1 pt) Library/TCNJ/TCNJ LinearSystems/problem8pg The system 3 x 15 y z 4 9 x + 44 y z 1 5x + 25 3 has the solution,, z 72 (1 pt) Library/TCNJ/TCNJ LinearSystems/problem16pg Determine whether the following systems have no solution, an infinite number of solutions or a unique solution? 3 5x + 7 7 6x 4 10 29 x + 9 47 5x + 7 7 6x 4 10 29 x + 9 50 5x + 10 15 3x + 6 9 7x + 14 21 73 (1 pt) Library/TCNJ/TCNJ LinearSystems/problem3pg Give a geometric description of the following systems of equations? 3 5x 5 8 4x + 2 2 75 (1 pt) Library/TCNJ/TCNJ LinearSystems/problem12pg x 2y + 9z 3 x 7y + 9z 13 3x 11y + 27z k In order for the above system of equations to be a consistent system, then k must be equal to 76 (1 pt) Library/TCNJ/TCNJ LinearSystems/problem5pg Determine whether the following system has no solution, an infinite number of solutions or a unique solution? 3 3x + 7 8 6x 3 1 6x 12 15 8x 16 20 6x 12 15 8x 16 18 77 (1 pt) Library/TCNJ/TCNJ LinearSystems/problem9pg The system 5x + 2 0 5x + 5 0 has the solution:, 78 (1 pt) Library/TCNJ/TCNJ LinearSystems/problem10pg Give a geometric description of the following system of equations? 3 x + 5 3 4x + 7 19 x + 11 17 16x 8 4 8x + 4 2 24x 12 6 x + 5 3 4x + 7 19 x + 11 19 74 (1 pt) Library/TCNJ/TCNJ LinearSystems/problem11pg Give a geometric description of the following systems of equations 2x 10 6 5x 25 12 2x 10 6 5x 25 15 9? 3 2x 4 12 5x + 3 10 2x 4 12 3x + 6 15 2x 4 12 3x + 6 18 79 (1 pt) Library/TCNJ/TCNJ LinearSystems/problem6pg Give a geometric description of the following systems of equations x + 3y + 8z 5 4x 11y 26z 4 3x + 9y + 21z 5 7x + 7y + 5z 1 4x 3y + z 3 15x 13y 3z 12

? 3? 4 7x + 7y + 5z 1 4x 3y + z 3 15x 13y 3z 7 8x + 10y 4z 4 20x 25y + 10z 10 28 x + 35 y 14 z 14 80 (1 pt) Library/TCNJ/TCNJ LinearSystems/problem17pg Determine whether the following system has no solution, an infinite number of solutions or a unique solution? 3? 4 3 x + y + 5 z 3 3x 5y + 4z 3 9x 15y 17z 21 6x 15y + 3z 6 8x + 20y 4z 8 12x + 30y 6z 12 3 x + y + 5 z 3 3x 5y + 4z 3 9x 15y 17z 20 x + 4y + 16z 1 x 3y 12z 2 4x + 16y + 60z 6 81 (1 pt) Library/TCNJ/TCNJ SolutionSetsLinearSystems- /problem7pg 1 3 2-2 -4 1 Let A 0 0 1-4 0 4 0 0 0 0 1-1 0 0 0 0 0 0 Describe all solutions of A 0 +x 4 +x 6 82 (1 pt) Library/TCNJ/TCNJ SolutionSetsLinearSystems- /problem1pg Find a set of vectors u, v in R 4 that spans the solution set of the equations: u x y w 0 3x + 2y + z + 3w 0, v 83 (1 pt) Library/TCNJ/TCNJ SolutionSetsLinearSystems- /problem8pg Suppose the solution set of a certain system of equations can be described as x 1 1 + 5t, 2 + 4t, x 3 6 + 4t, where t is a free variable Use vectors to describe this set as a line in R 4 +t 84 (1 pt) Library/TCNJ/TCNJ SolutionSetsLinearSystems- /problem9pg -3-12 Given A -2-8 2 8 find one nontrivial solution of A 0 by inspection 85 (1 pt) Library/TCNJ/TCNJ SolutionSetsLinearSystems- /problem6pg 1 3 4-1 Let A 2 6 8-2 Describe all solutions of A 0 +x 3 +x 4 86 (1 pt) Library/TCNJ/TCNJ RowReduction/problem4pg 6x 10 6 21x 35 k For the above system of equations to be consistent, k must equal 87 (1 pt) Library/TCNJ/TCNJ RowReduction/problem7pg If the following system 4x 4 10 10x + k 22 is consistent, then k 88 (1 pt) Library/TCNJ/TCNJ RowReduction/problem8pg For the following system to be consistent, 6x + 5y 3z 5 7x 8y + k z 3 34x + 37y 23z 18 we must have, k 10

89 (1 pt) Library/TCNJ/TCNJ RowReduction/problem3pg Determine all values of h and k for which the system 5x + 5y 7z 3 4x + 7y 7z 2 31x + 13y + hz k has no solution k h 90 (1 pt) Library/TCNJ/TCNJ RowReduction/problem11pg Let k,h be unknown constants and consider the linear system: 4x + 5y 5z 4 5x + 8y + 2z 6 6x 21y + hz k This system has a unique solution whenever h If h is the (correct) value entered above, then the above system will be consistent for how many value(s) of k? A no values B a unique value C infinitely many values 91 (1 pt) Library/TCNJ/TCNJ RowReduction/problem12pg Let k,h be unknown constants and consider the linear system: x + 3 h 8x + k 10 This system has a unique solution whenever k If k is the (correct) value entered above, then the above system will be consistent for how many value(s) of h? A no values B infinitely many values C a unique value 92 (1 pt) Library/TCNJ/TCNJ RowReduction/problem5pg Suppose that the following 12x 6 12 28x 14 k 20 x 10 20 is a consistent system Then k 93 (1 pt) Library/TCNJ/TCNJ RowReduction/problem9pg If the following system is consistent, 11 4x + 4 0 k x + 12 3 then k 94 (1 pt) Library/TCNJ/TCNJ RowReduction/problem10pg If the following system has infinitely many solutions, 6x + 5y 7z 7 5x 7y + 2z 9 8x + 29y + hz k then k, h 95 (1 pt) Library/TCNJ/TCNJ RowReduction/problem6pg If there are an infinite number of solution to the system 7x + 9 h 8x + k 1 then k, h 96 (1 pt) Library/TCNJ/TCNJ MatrixEquations/problem2pg Perform one step of row reduction, in order to calculate the values for x and y by back substitution Then calculate the values for x and for y Also calculate the determinant of the original matrix You can let webwork do much of the calculation for you if you want (eg enter 45-(56/76)(-3) instead of calculating the value out) You can also use the preview feature in order to make sure that you have used the correct syntax in entering the answer Note since the determinant is unchanged by row reduction it will be easier to calculate the determinant of the row reduced matrix 1-3 x 4 3 y 1-3 0 det 1-1 x y 97 (1 pt) Library/TCNJ/TCNJ MatrixEquations/problem4pg Let A 4-5 4-3 -2-5 and -3-2 -3 1-4 5 What does Ax mean? 98 (1 pt) Library/TCNJ/TCNJ MatrixEquations/problem11pg To see if b 3 16 is a linear combination of the vectors 6 a 1 4 3 and a 2 6 10 3-6 one can solve the matrix equation A c where the columns of 1

A are v 1 and v 2 and c 99 (1 pt) Library/TCNJ/TCNJ MatrixEquations/problem12pg 5 To see if b is a linear combination of the vectors -5 2 10 a 1 and a -1 2 7 one can solve the matrix equation A c where the columns of A are v 1 and v 2 and c 100 (1 pt) Library/TCNJ/TCNJ MatrixEquations/problem10pg -1 Let A be a 3x2 matrix Suppose we know that u and -4 1 v satisfy the equations Au a and Av b Find a solution x to A 4a + 2b 3 101 (1 pt) Library/TCNJ/TCNJ Dets CramersRule Misc- /problem2pg using Cramer s Rule det z 2x + 6y + 25z 4 9x 23y 97z 5 6x + 18y + 78z 5 102 (1 pt) Library/TCNJ/TCNJ Dets CramersRule Misc- /problem1pg using Cramer s Rule det 5x 2 2 6x 1 103 (1 pt) Library/TCNJ/TCNJ MatrixInverse/problem17pg For each section, find the matrix X solving the given equation 7 0-1 1 a X X 0 1-9 -8 0 1-10 4 b X X 1 0-8 7 1-1 8 4 c X X 0 1-10 -2 1-4 -1 7 d X X 2-7 5-4 e 1 0 0-3 -2 7 0 1 0 X 10 2 7 X 0 0 6 1 7 7 f g 0 0 1 0 1 0 1 0 0 1 0 0 0 1 0 0 4 1 X X -2-6 8 4 3-1 -9 1 8 2 10-7 -2 7 1 5-8 -8 X 104 (1 pt) Library/TCNJ/TCNJ VectorEquations/problem2pg Write a vector equation x+ y+ z that is equivalent to the system of equations: 7x + y 3z 9 3x + 9y + 7z 9 2x 3y 4z 6 X Generated by c WeBWorK, http://webworkmaaorg, Mathematical Association of America 12