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mathematics
college algebra graphs and models

Questions and Answers of College Algebra Graphs And Models

In Exercises 1–12, find the products AB and BA to determine whether B is the multiplicative inverse of A. A -4 0 1 3 B -2 4 0 1
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
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
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
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],
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
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
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 =
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
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
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
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
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
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
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
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
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
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
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
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
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 = +
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
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
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)]

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