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College Algebra 7th Edition Robert F Blitzer - Solutions

In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. 5x - 11y + 62 = = 12 -x + 3y - 2z = = -4 4 3x - 5y + 2z =
In Exercises 3–6, letCarry out the indicated operations.AB A = 3 1 1 0 2 1 B = 1 [2 1. and C= 1 [43] -1 3
Fill in each blank so that the resulting statement is true.Using Gauss-Jordan elimination to solve the systemwe obtain the matrixThe system’s solution set is___________ . y + z = 5x + y2z: 2x - 3y + 4z = -4 12 -15,
Fill in each blank so that the resulting statement is true.True or false: If {(2z + 3, 5z - 1, z)} is the solution set of a system with dependent equations, then (5, 4, 1) is a solution of this system.________
Solve each equation or inequality in Exercises 1–6.3x3 + 8x2 - 15x + 4 = 0
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. w w + x 3w + 4x 2x - y - 3z = -9 y 0 6 3 - + 2x - 2y + z z =
In Exercises 9–16, find the following matrices:a. A + Bb. A - Bc. -4Ad. 3A + 2B. A 4 3 B = 5 9 0 7
In Exercises 6–10, perform the indicated matrix operations or solve the matrix equation for X given that A, B, and C are defined as follows. If an operation is not defined, state the reason.A(BC) A = 02 -1 3 10 B = [ 4 -6 c=[+] C = 0 1
In Exercises 8–11, use Gaussian elimination to find the complete solution to each system, or show that none exists. x - 3y + z = -2x + y + 3z 4y + 2z = X 1 -7 0
Evaluate each determinant in Exercises 1–10. 165 -6 5 9-
In Exercises 5–8, find values for the variables so that the matrices in each exercise are equal. X 2z y * + 3] = [¹2 8 [12 57 68
In Exercises 1–12, find the products AB and BA to determine whether B is the multiplicative inverse of A. A = -2 -5 1 -1 2-1 3-1 1 B = 10 1 2 1 3 -1 1 1
In Exercises 9–12, write the system of linear equations represented by the augmented matrix. Use x, y, and z, or, if necessary, w, x, y, and z, for the variables. 5 0 01-4 72 3 0 -11 12 3
Evaluate: 4 0 5 -1 52 3 -1 4
Evaluate each determinant in Exercises 1–10. 1234 1 1718
In Exercises 1–12, find the products AB and BA to determine whether B is the multiplicative inverse of A. A = 1 2 1 1 4 343 B || = | | 72 TINTIN -3 1 121212 1
Solve for x only using Cramer’s Rule: 3x + y - 2z у - 2z = 2x + 7y + 3z = 4x-3y - z = -3 9 7.
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. 3 2wx2yz = 2x + y + z = 4 8x + 7y + 5z = 13 6 w -W 3w+x2y + 2z =
In Exercises 9–12, write the system of linear equations represented by the augmented matrix. Use x, y, and z, or, if necessary, w, x, y, and z, for the variables. 7 0 4 01 -5 27 0 -13 11 6
Fill in each blank so that the resulting statement is true.To find the multiplicative inverse of an invertible matrix A, we perform row operations on [A| In] to obtain a matrix of the form [In| B], where B =_______ .
If f(x) = √4x - 7, find f-1(x).
Fill in each blank so that the resulting statement is true.True or false: Matrices of different orders can sometimes be multiplied._________
Fill in each blank so that the resulting statement is true.If the matrix equation AX = B has a unique solution, then we can solve the equation using X =_________ .
Graph: f(x) = X/x2-16.
Fill in each blank so that the resulting statement is true.If A is an m × n matrix and B is an n × p matrix, then AB is defined as an_______ × ________matrix. To find the product AB, the number of________ in matrix A must equal the number of________ in matrix B.
In Exercises 8–11, use Gaussian elimination to find the complete solution to each system, or show that none exists. x1 + 4x2 + 3x3 - 6х4 - - 3 X1 + 3x2 + X3 - 4х4 2x1 + 8x2 + 7x3 - 5х4 - 11 2x1 + 5x2 - 6x4 4 5 U
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. 2w x y w - 3x + 2y 3w w + 2x - 4y - Z 3 = -4 x3y + z = 1 4yz = -2
Use the graph of f(x) = 4x4 - 4x3 - 25x2 + x + 6 shown in the figure to factor the polynomial completely. f(x) = 4x4 - 4x³ 25x² + x + 6 y HF #B 20- 10 1³---10 -20- -30- -40- -50- -60- LOLIT II H X
In Exercises 9–16, find the following matrices:a. A + Bb. A - Bc. -4Ad. 3A + 2B. A = 2 14 4 -10 12 -2 -2 10 2 B = 6 0 -5 -2 -4 2 -2 10 -12
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. 2w z = 0 z = 0 3w+ 2x + 4y 5w - 2x - 2y z = 0 2w + 3x - 7y - 5z = 0 - x + 3y + -
In Exercises 13–18, use the fact that if 1 ad - bc A then 1 = [a b], th -b] 10 to find the inverse of each matrix, if d -b a A-¹ possible. Check that AA¹ = 1₂ and A¹A = 1₂. bc-c
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. 2x + y - z = 2 (3x+3y - 2z = 3
In Exercises 16–19, graph each equation, function, or inequality in rectangular coordinate system. y = -3x - 1
In Exercises 9–16, find the following matrices:a. A + Bb. A - Bc. -4Ad. 3A + 2B. 1 A = 3 5 3 4 6 2 -1 [1] -2 0 B = 3
In Exercises 13–18, use the fact that if 1 ad - bc A then 1 = [a b], th -b] 10 to find the inverse of each matrix, if d -b a A-¹ possible. Check that AA¹ = 1₂ and A¹A = 1₂. bc-c
The figure shows the intersections of three one-way streets. The numbers given represent traffic flow, in cars per hour, at a peak period (from 4 p.m. to 6 p.m.).a. Use the idea that the number of cars entering each intersection per hour must equal the number of cars leaving per hour to set up a
For Exercises 11–22, use Cramer’s Rule to solve each system. x + 2y = 3 3x - 4y = 4
In Exercises 14–27, perform the indicated matrix operations given that A, B, C, and D are defined as follows. If an operation is not defined, state the reason.2B A = [2 -1 5 3 12 C = -1 1 3 2 -1 2 1 2 B = D = 0 3 T -2 2 -5 -2 3 1 3 -2 4
For Exercises 11–22, use Cramer’s Rule to solve each system. 2x + y = 3 x - y = 3
For Exercises 11–22, use Cramer’s Rule to solve each system. [4x - 5y = 17 (2x + 3y = 3
In Exercises 13–18, perform each matrix row operation and write the new matrix. 1 -3 2 0 3 1 -17 2 -2 13 132 -3R₁ + R₂
In Exercises 1–12, find the products AB and BA to determine whether B is the multiplicative inverse of A. A = 00-2 1 01 -1 10 -1 0 1 0 0 -1 B = 203 1 1 1 0 1 2 02 1 01 0 1
In Exercises 16–19, graph each equation, function, or inequality in rectangular coordinate system.f(x) = x2 - 2x - 3
In Exercises 9–12, write the system of linear equations represented by the augmented matrix. Use x, y, and z, or, if necessary, w, x, y, and z, for the variables. 4 1 5 1 -1 0 3 0 0 0 0 11 دیا 1 -18 74 5 3
For Exercises 11–22, use Cramer’s Rule to solve each system. [x + y = 7 [x - y = 3
In Exercises 8–11, use Gaussian elimination to find the complete solution to each system, or show that none exists. (2x + 3y - 5z - = 15 4 x + 2y z =
In Exercises 9–12, write the system of linear equations represented by the augmented matrix. Use x, y, and z, or, if necessary, w, x, y, and z, for the variables. 1 1 4 -1 1 -1 20 00 1 3 0 7 0 5 11 12 4 5
Graph y = log2 x and y = log2(x + 1) in the same rectangular coordinate system.
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. w + xy + 2w x + 2y - -w + 2x + y + y + z z 2z z = -2 7 -1
In Exercises 14–27, perform the indicated matrix operations given that A, B, C, and D are defined as follows. If an operation is not defined, state the reason.-5(A + D) A = [2 -1 5 3 12 C = -1 1 3 2 -1 2 1 2 B = D = 0 3 T -2 2 -5 -2 3 1 3 -2 4
In Exercises 21–38, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. z = -2 x + y 2xy + z = -x + 2y + 2z = 25 5 1
For Exercises 11–22, use Cramer’s Rule to solve each system. 3x = 7y + 1 2х = 3у Зу - 1
In Exercises 17–26, letSolve each matrix equation for X.3X + A = B A = -3 -7 2 -9 5 0 and B = -5 -1 0 0 3 -4
In Exercises 19–28, find A-1 by forming [A| I] and then using row operations to obtain [I| B], where A-1 = [B]. Check that AA-1 = I and A-1 A = I. A = 3 00 090 009
In Exercises 19–28, find A-1 by forming [A| I] and then using row operations to obtain [I| B], where A-1 = [B]. Check that AA-1 = I and A-1 A = I. A = 1 -2 1 2 -1 0 1 -1 0
In Exercises 17–26, letSolve each matrix equation for X.3X + 2A = B A = -3 -7 2 -9 5 0 and B = -5 -1 0 0 3 -4
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. 2w 3x + 4y + z z W - 3w+ x - 2y 2z = 7 x + 3y - 5z = 10 6 -
In Exercises 19–28, find A-1 by forming [A| I] and then using row operations to obtain [I| B], where A-1 = [B]. Check that AA-1 = I and A-1 A = I. A || 1 -1 0 2 2 3 1 -1 0
In Exercises 14–27, perform the indicated matrix operations given that A, B, C, and D are defined as follows. If an operation is not defined, state the reason.AB A = [2 -1 5 3 12 C = -1 1 3 2 -1 2 1 2 B = D = 0 3 T -2 2 -5 -2 3 1 3 -2 4
In Exercises 21–38, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. x - 2y 2x - -x + 24 z = y + z = y2z = -4
For Exercises 11–22, use Cramer’s Rule to solve each system. [2x = 3y + 2 5x = 51 - 4y
In Exercises 21–38, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. 0 x + 3y x + y + z = 1 3x y z = 11 -
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. w + 2x + 3y - z = 7 2x - 3y + z = 4 = 3 w - W 4x + y
In Exercises 14–27, perform the indicated matrix operations given that A, B, C, and D are defined as follows. If an operation is not defined, state the reason.BA A = [2 -1 5 3 12 C = -1 1 3 2 -1 2 1 2 B = D = 0 3 T -2 2 -5 -2 3 1 3 -2 4
For Exercises 11–22, use Cramer’s Rule to solve each system. у y = -4x + 2 2x = 3у + 8
In Exercises 17–26, letSolve each matrix equation for X.2X + 5A = B A = -3 -7 2 -9 5 0 and B = -5 -1 0 0 3 -4
In Exercises 19–28, find A-1 by forming [A| I] and then using row operations to obtain [I| B], where A-1 = [B]. Check that AA-1 = I and A-1 A = I. A = 2 2 0 3 -2 -1 -1 -1 1
In Exercises 21–38, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. = z -1 z = -4 11 зу - x + 5y - + 6y + 2z. -3x =
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. W -M w 3w + z = 0 x 4x + y + 2z = 0 y + 2z = 0 2
In Exercises 14–27, perform the indicated matrix operations given that A, B, C, and D are defined as follows. If an operation is not defined, state the reason.BD A = [2 -1 5 3 12 C = -1 1 3 2 -1 2 1 2 B = D = 0 3 T -2 2 -5 -2 3 1 3 -2 4
Evaluate each determinant in Exercises 23–28. 3 2 2 0 1 1 5 01 -5 -1
In Exercises 17–26, letSolve each matrix equation for X.B - X = 4A A = -3 -7 2 -9 5 0 and B = -5 -1 0 0 3 -4
In Exercises 14–27, perform the indicated matrix operations given that A, B, C, and D are defined as follows. If an operation is not defined, state the reason.DB A = [2 -1 5 3 12 C = -1 1 3 2 -1 2 1 2 B = D = 0 3 T -2 2 -5 -2 3 1 3 -2 4
Evaluate each determinant in Exercises 23–28. 4 3 2 00 4 5 -1 -3
In Exercises 17–26, letSolve each matrix equation for X.A - X = 4B A = -3 -7 2 -9 5 0 and B = -5 -1 0 0 3 -4
In Exercises 14–27, perform the indicated matrix operations given that A, B, C, and D are defined as follows. If an operation is not defined, state the reason.3A + 2D A = [2 -1 5 3 12 C = -1 1 3 2 -1 2 1 2 B = D = 0 3 T -2 2 -5 -2 3 1 3 -2 4
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. 3xy + 4z = 8 y + 2z = 1
In Exercises 13–18, perform each matrix row operation and write the new matrix. 1 -5 0 3 -4 10 2 -2 -3 -1 2 -1 0 1 4 0 6 2 -3 -3R₁ + R₂ 4R₁ + R4
For Exercises 11–22, use Cramer’s Rule to solve each system. (2x- 2х - 9y = 5 (3x-3y = 11 Зу
In Exercises 17–26, letSolve each matrix equation for X.2X + A = B A = -3 -7 2 -9 5 0 and B = -5 -1 0 0 3 -4
In Exercises 19–28, find A-1 by forming [A| I] and then using row operations to obtain [I| B], where A-1 = [B]. Check that AA-1 = I and A-1 A = I. A = 200 04 0 006
In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. 5y + 5y + x + 2y - -2x - 10z 10z = 19 4z = 12
In Exercises 19–20, a few steps in the process of simplifying the given matrix to row-echelon form, with 1s down the diagonal from upper left to lower right, and 0s below the 1s, are shown. Fill in the missing numbers in the steps that are shown. 1 2 -3 -2 3 1
Use synthetic division to divide x3 - 6x + 4 by x - 2.
In Exercises 19–28, find A-1 by forming [A| I] and then using row operations to obtain [I| B], where A-1 = [B]. Check that AA-1 = I and A-1 A = I. 24-4 A 1 3 2 4 -4 -3
In Exercises 21–38, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. 2x y y z = - 4 x + y - 5z = -4 X - 2y 4
In Exercises 25–28, the first screen shows the augmented matrix, A, for a non square linear system of three equations in four variables, w, x, y, and z. The second screen shows the reduced row-echelon form of matrix A. For each exercise,a. Write the system represented by A.b. Use the reduced
In Exercises 43–44,a. Write each linear system as a matrix equation in the form AX = B.b. Solve the system using the inverse that is given for the coefficient matrix. X y + 2z = 12 y X - z = + 2z -5 = 10 The inverse of 1 O 1 -1 2 1 -1 is O 2 2 -1 T 2 O
In Exercises 29–32, write each linear system as a matrix equation in the form AX = B, where A is the coefficient matrix and B is the constant matrix. x + 4y z = 3 = 5 = 12 x + 3y2z 2x + 7y5z
In Exercises 41–42, evaluate each determinant. 3 1 -2 3 13 0 7 7 |9 3 0 51 -61 5
In Exercises 29–32, write each linear system as a matrix equation in the form AX = B, where A is the coefficient matrix and B is the constant matrix. 6x + 5y = 13 5x + 4y = 10
Evaluate each determinant in Exercises 23–28. 3 1 -3 4 -1 3 0 0 -5
In Exercises 17–26, letSolve each matrix equation for X.4A + 3B = -2X A = -3 -7 2 -9 5 0 and B = -5 -1 0 0 3 -4
In Exercises 14–27, perform the indicated matrix operations given that A, B, C, and D are defined as follows. If an operation is not defined, state the reason.AB - BA A = [2 -1 5 3 12 C = -1 1 3 2 -1 2 1 2 B = D = 0 3 T -2 2 -5 -2 3 1 3 -2 4
Describe what happens when Gaussian elimination is used to solve an inconsistent system.
In Exercises 45–48, solve each equation for x. -2 X 4 6 = 32
Write a system of linear equations in three or four variables to solve Exercises 47–50. Then use matrices to solve the system.A furniture company produces three types of desks: a children’s model, an office model, and a deluxe model. Each desk is manufactured in three stages: cutting,
In Exercises 51–52, use the coding matrixto encode and then decode the given message.LOVE A = 4 -3 and its inverse A-¹ = 3 4]
Exercises 50–52 will help you prepare for the material covered in the next section. In each exercise, perform the indicated operation or operations.1/2 [8 - (-8)]
What is the difference between Gaussian elimination and Gauss-Jordan elimination?

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