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College Algebra 7th Edition Robert F Blitzer - Solutions

Evaluate each determinant in Exercises 37–40. 4 28 -2 04 -7 1 500 5 400 -1
In Exercises 37–42,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 + 2y + 5z = 2 2x + 3y + 8z = 3 -x + y + 2z = 3 The inverse of [1 1 2 -1 25 38 1 1 2 is 2-1 -1 12 -7 -2 -5 3 1
In Exercises 37–44, perform the indicated matrix operations given that A, B, and C are defined as follows. If an operation is not defined, state the reason.4B - 3C А= 4 0 5 1 -3 0 B 5 1 1 −1 -[A] - [1] -2 -2 C
Evaluate each determinant in Exercises 37–40. 3 -2 2 1 1 21 0 0 0 -2 2 -1 -1 4 3 3
In Exercises 37–42,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. 2x + 6y + 6z = = 8 2x + 7y + 6z 10 2x + 7y + 7z = 9 = The inverse of 2 6 6 2 7 6 is 277 TIN O -3 0-1
In Exercises 37–42,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 + z = 2y - z 2x + 3y = = 8 -7 1 The inverse of 1 -1 O 2 1 H O 2-1 3 3 3 is-2 325 -2 -4 -5 2
In Exercises 37–38, find the products AB and BA to determine whether B is the multiplicative inverse of A. A = [²₂7] 1 B 4 -1 -7] 3
In Exercises 37–38, find the products AB and BA to determine whether B is the multiplicative inverse of A. A = 1 0 0 0 2 -1 0 -7 4 1 B = 0 0 00 4 7 1 2
Evaluate each determinant in Exercises 37–40. -2 1 1 2 -3 3 -4 0 2 2 0 1 5 0 -3 1
In Exercises 37–44, perform the indicated matrix operations given that A, B, and C are defined as follows. If an operation is not defined, state the reason.5C - 2B А= 4 0 5 1 -3 0 B 5 1 1 −1 -[A] - [1] -2 -2 C
In Exercises 37–44, perform the indicated matrix operations given that A, B, and C are defined as follows. If an operation is not defined, state the reason.BC + CB А= 4 0 5 1 -3 0 B 5 1 1 −1 -[A] - [1] -2 -2 C
a. The figure shows the intersections of a number of one-way streets. The numbers given represent traffic flow at a peak period (from 4 p.m. to 5:30 p.m.). Use the figure to write a linear system of six equations in seven variables based on the idea that at each intersection the number of cars
In Exercises 39–42, find A-1. Check that AA-1 = I and A-1 A = I. Α = 1 -2 -1 3
Evaluate each determinant in Exercises 37–40. 1 -3 -3 -1 2 1 3 2 0 2 032 -2 0 -2 1 0
In Exercises 37–42,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 2x 4x 6y + 3z = 11 7y + 3z = 14 12y + 5z = 25 The inverse of 1 -6 3 2 4 1 -7 3 is 2 -12 5 4 -6 3 -7 3 -12 5
In Exercises 37–42,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. w - x + 2y - x = -w + xy + 2z The inverse of 1 O -1 -x + y - 2z -1 2 1 -1 1 -1 y + z = -1 = -3 4 2 -4 1 2 1
In Exercises 39–42, find A-1. Check that AA-1 = I and A-1 A = I. 10 A = 2 1 10 -2 0 -3
In Exercises 37–44, perform the indicated matrix operations given that A, B, and C are defined as follows. If an operation is not defined, state the reason.A(B + C) А= 4 0 5 1 -3 0 B 5 1 1 −1 -[A] - [1] -2 -2 C
In Exercises 37–42,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. 2w 3w -w + x - 2y + z = 4 4w - x + y = 6 The inverse of 2 3 -1 4 + y + z = 6 + z = 9 -1 0 0 1 -2 1 1 1 0
In Exercises 39–42, find A-1. Check that AA-1 = I and A-1 A = I. A = Го 5 3
In Exercises 41–44, determine whether each statement makes sense or does not make sense, and explain your reasoning.I omitted row 3 fromand expressed the system in the form 1 0 0 0 -1 -2 1 -10-1 0 5 2
In Exercises 41–44, determine whether each statement makes sense or does not make sense, and explain your reasoning.I omitted row 3 fromand expressed the system in the form 0 0 -1 1 0 -2 -10 0 2 -1 0
Find the quadratic function f(x) = ax2 + bx + c for which f(-2) = -4, f(1) = 2, and f(2) = 0.
In Exercises 41–42, evaluate each determinant. 5 0 4 -3 17 -5 4 6 -1 0 4 -3 -1 1 5
Describe what happens when Gaussian elimination is used to solve a system with dependent equations.
In Exercises 39–42, find A-1. Check that AA-1 = I and A-1 A = I. 1 A = 4 5 3-2 -7 -8 13 16
In Exercises 43–44, write the system of linear equations for which Cramer’s Rule yields the given determinants. D - 2 3 5 Dx 8 -10 -4 5
In Exercises 37–44, perform the indicated matrix operations given that A, B, and C are defined as follows. If an operation is not defined, state the reason.A - C А= 4 0 5 1 -3 0 B 5 1 1 −1 -[A] - [1] -2 -2 C
In Exercises 43–44, find A-1 and check. A = et ex -e³x ex
Find the quadratic function f(x) = ax2 + bx + c for which f(-1) = 5, f(1) = 3, and f(2) = 5.
In solving a system of dependent equations in three variables, one student simply said that there are infinitely many solutions. A second student expressed the solution set as {(4z + 3, 5z - 1, z)}. Which is the better form of expressing the solution set and why?
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 = y + 3z = - 2z: = 3x 7 -2 0 The inverse of 1 1 2 1 3 is O O 3 -2 -2 9 -3 2 83 -8 3 1 -3 1
In Exercises 43–44, write the system of linear equations for which Cramer’s Rule yields the given determinants. D = 2 5 -3. 6 Dx 8 11 -3 6
In Exercises 37–44, perform the indicated matrix operations given that A, B, and C are defined as follows. If an operation is not defined, state the reason.B - A А= 4 0 5 1 -3 0 B 5 1 1 −1 -[A] - [1] -2 -2 C
In Exercises 37–44, perform the indicated matrix operations given that A, B, and C are defined as follows. If an operation is not defined, state the reason.A(BC) А= 4 0 5 1 -3 0 B 5 1 1 −1 -[A] - [1] -2 -2 C
Find the cubic function f(x) = ax3 + bx2 + cx + d for which f(-1) = 0, f(1) = 2, f(2) = 3, and f(3) = 12.
In Exercises 43–44, find A-1 and check. A = = e²t Le³x -et e²r
Find the cubic function f(x) = ax3 + bx2 + cx + d for which f(-1) = 3, f(1) = 1, f(2) = 6, and f(3) = 7.
In Exercises 37–44, perform the indicated matrix operations given that A, B, and C are defined as follows. If an operation is not defined, state the reason.A(CB) А= 4 0 5 1 -3 0 B 5 1 1 −1 -[A] - [1] -2 -2 C
In Exercises 41–44, determine whether each statement makes sense or does not make sense, and explain your reasoning.I solved a non square system in which the number of equations was the same as the number of variables.
In Exercises 41–44, determine whether each statement makes sense or does not make sense, and explain your reasoning.Models for controlling traffic flow are based on an equal number of cars entering an intersection and leaving that intersection.
Consider the linear systemFor which values of a will the system be inconsistent? x + 3y + z = 2x + 5y + 2az = x + y + a²z = a² 0 -9.
A ball is thrown straight upward. A position functioncan be used to describe the ball’s height, s(t), in feet, after t seconds.a. Use the points labeled in the graph to find the values of a, v0, and s0. Solve the system of linear equations involving a, v0, and s0 using matrices.b. Find and
A football is kicked straight upward. A position functioncan be used to describe the ball’s height, s(t), in feet, after t seconds.a. Use the points labeled in the graph to find the values of a, v0, and s0. Solve the system of linear equations involving a, v0, and s0 using matrices.b. Find and
In Exercises 45–46, if I is the multiplicative identity matrix of order 2, find (I - A)-1 for the given matrix A. 8-5 -3 2
Use the coding matrixand its inverseto encode and then decode the word RULE. A 3 4 2 3
In Exercises 45–50, letFind the product of the sum of A and B and the difference between C and D. A = D = 금화 [ -1 0 -1 대와 공원 C 0 1 B = 와
Write a system of linear equations in three or four variables to solve Exercises 47–50. Then use matrices to solve the system.Three foods have the following nutritional content per ounce.If a meal consisting of the three foods allows exactly 660 calories, 25 grams of protein, and 425 milligrams
In Exercises 45–48, solve each equation for x. x +3 -6 x-2-4 28
In Exercises 45–46, if I is the multiplicative identity matrix of order 2, find (I - A)-1 for the given matrix A. 7 -57 -4 3
In Exercises 45–50, letFind the product of the difference between A and B and the sum of C and D. A = D = 금화 [ -1 0 -1 대와 공원 C 0 1 B = 와
In Exercises 47–48, find (AB)-1, A-1 B-1, and B-1 A-1. What do you observe? A = 23 2 نا دیا (3 1 B = 4 1 71 2
In Exercises 45–48, solve each equation for x. 1 3 1 در - 0 -2 -2 1 = -8 2
In Exercises 46–51, evaluate each determinant. 3 -1 21 5
In Exercises 46–51, evaluate each determinant. -2 -3 -4 -8
In Exercises 45–48, solve each equation for x. 2 -3 2 x 1 1 0 1 4 = 39 =
Write a system of linear equations in three or four variables to solve Exercises 47–50. Then use matrices to solve the system.The bar graph shows the number of rooms, bathrooms, fireplaces, and elevators in the U.S. White House.Combined, there are 198 rooms, bathrooms, fireplaces, and elevators.
Write a system of linear equations in three or four variables to solve Exercises 47–50. Then use matrices to solve the system.Imagine the entire global population as a village of precisely 200 people. The bar graph shows some numeric observations based on this scenario.Combined, there are 183
In Exercises 47–48, find (AB)-1, A-1 B-1, and B-1 A-1. What do you observe? A 2-9 1 -4 B = 95
In Exercises 45–50, letUse any three of the matrices to verify a distributive property. A = D = 금화 [ -1 0 -1 대와 공원 C 0 1 B = 와
In Exercises 46–51, evaluate each determinant. ON 0 22 222 NNNN 0 0 2 2 0 0 2
The + sign in the figure is shown using 9 pixels in a 3 × 3 grid. The color levels are given to the right of the figure. Each color is represented by a specific number: 0, 1, 2, or 3. Use this information to solve Exercises 51–52.a. Find a matrix that represents a digital photograph of the +
In Exercises 45–50, letUse any three of the matrices to verify an associative property.In Exercises 49–50, suppose that the vertices of a computer graphic are points, (x, y), represented by the matrixFind BZ and explain why this reflects the graphic about the x-axis. A = D
In Exercises 46–51, evaluate each determinant. 2 1 -2 4 -1 4 -3 ՄԱՁ 5
Determinants are used to find the area of a triangle whose vertices are given by three points in a rectangular coordinate system. The area of a triangle with vertices (x1, y1), (x2 , y2), and (x3 , y3) iswhere the ± symbol indicates that the appropriate sign should be chosen to yield a positive
You are choosing between two cellphone plans. Data Plan A offers a flat monthly rate of $20 per gigabyte (GB). Data Plan B has a monthly fee of $40 with a charge of $15 per GB. For how many GB of data will the costs for the two data plans be the same? What will be the cost for each plan?
Determinants are used to find the area of a triangle whose vertices are given by three points in a rectangular coordinate system. The area of a triangle with vertices (x1, y1), (x2 , y2), and (x3 , y3) iswhere the ± { symbol indicates that the appropriate sign should be chosen to yield a
In Exercises 45–50, letUse any three of the matrices to verify an associative property. A = D = 금화 [ -1 0 -1 대와 공원 C 0 1 B = 와
In Exercises 45–50, letIn Exercises 49–50, suppose that the vertices of a computer graphic are points, (x, y), represented by the matrix Find CZ and explain why this reflects the graphic about the y-axis. A = D = 금화 [ -1 0 -1 대와 공원 C 0 1 B = 와
In Exercises 46–51, evaluate each determinant. 4 -5 7 6 32 0 -4
The + sign in the figure is shown using 9 pixels in a 3 × 3 grid. The color levels are given to the right of the figure. Each color is represented by a specific number: 0, 1, 2, or 3. Use this information to solve Exercises 51–52.a. Find a matrix that represents a digital photograph of the +
Determinants are used to show that three points lie on the same line (are collinear). Ifthen the points (x1 , y1), (x2 , y2), and (x3 , y3) are collinear. If the determinant does not equal 0, then the points are not collinear. Use this information to work Exercises 51–52.Are the points (3, -1),
Find the inverse of f(x) = 3x - 4.
In Exercises 51–52, use the coding matrixto encode and then decode the given message.HELP A = 4 -3 and its inverse A-¹ = 3 4]
In Exercises 46–51, evaluate each determinant. |1 0 0 0 1 3 -24 0 2 2 1 0 301
A chemist needs to mix a 75% saltwater solution with a 50% saltwater solution to obtain 10 gallons of a 60% saltwater solution. How many gallons of each of the solutions must be used?
Determinants are used to show that three points lie on the same line (are collinear). Ifthen the points (x1 , y1), (x2 , y2), and (x3 , y3) are collinear. If the determinant does not equal 0, then the points are not collinear. Use this information to work Exercises 51–52.Are the points (-4, -6),
In Exercises 53–54, use the coding matrixmessage. Check your result by decoding the cryptogram. A = A-¹ 1 3 0 -1 -1 0 0 0 2 and its inverse -1 12 12 to write a cryptogram for each 01-3
In Exercises 52–55, use Cramer’s Rule to solve each system. x - 2y = 8 (3x + 2y = -1
In Exercises 53–54, use the coding matrixmessage. Check your result by decoding the cryptogram. A = A-¹ 1 3 0 -1 -1 0 0 0 2 and its inverse -1 12 12 to write a cryptogram for each 01-3
Determinants are used to write an equation of a line passing through two points. An equation of the line passing through the distinct points (x1 , y1) and (x2 , y2) is given byUse this information to work Exercises 53–54.Use the determinant to write an equation of the line passing through (3, -5)
Determinants are used to write an equation of a line passing through two points. An equation of the line passing through the distinct points (x1 , y1) and (x2 , y2) is given byUse this information to work Exercises 53–54.Use the determinant to write an equation of the line passing through (-1, 3)
In Exercises 52–55, use Cramer’s Rule to solve each system. x + 2y + 2z = 5 2x + 4y + 7z = 19 -2x 5y2z = 8
In Exercises 52–55, use Cramer’s Rule to solve each system. 7x + 2y = 0 (2x + y = −3 -3
Exercises 50–52 will help you prepare for the material covered in the next section. In each exercise, perform the indicated operation or operations.-6 - (-5)
Use the quadratic function y = ax2 + bx + c to model the following data:Use Cramer’s Rule to determine values for a, b, and c. Then use the model to write a statement about the average number of automobile accidents in which 30-year-olds and 50-year-olds are involved daily. x (Age of a
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(-4) + 2(5) + 3(-6)
In Exercises 52–55, use Cramer’s Rule to solve each system. 2x + у 3x у - 27 - 2z || = -4 0 = -11
Each column in the matrix describes a point on the letter. The order of the columns shows the direction in which a pencil must move to draw the letter. The L is completed by connecting the last point in the matrix, (0, 5), to the starting point, (0, 0). Use these ideas to solve Exercises
Most graphing utilities can perform row operations on matrices. Consult the owner’s manual for your graphing utility to learn proper keystrokes for performing these operations. Then duplicate the row operations of any three exercises that you solved from Exercises 13–18Data from Exercise
Describe what is meant by the augmented matrix of a system of linear equations.
Each column in the matrix describes a point on the letter. The order of the columns shows the direction in which a pencil must move to draw the letter. The L is completed by connecting the last point in the matrix, (0, 5), to the starting point, (0, 0). Use these ideas to solve Exercises
In your own words, describe each of the three matrix row operations. Give an example with each of the operations.
Each column in the matrix describes a point on the letter. The order of the columns shows the direction in which a pencil must move to draw the letter. The L is completed by connecting the last point in the matrix, (0, 5), to the starting point, (0, 0). Use these ideas to solve Exercises 53–60.a.
Each column in the matrix describes a point on the letter. The order of the columns shows the direction in which a pencil must move to draw the letter. The L is completed by connecting the last point in the matrix, (0, 5), to the starting point, (0, 0). Use these ideas to solve Exercises
Describe how to use row operations and matrices to solve a system of linear equations.
Explain how to evaluate a second-order determinant.
What is the multiplicative identity matrix?
Each column in the matrix describes a point on the letter. The order of the columns shows the direction in which a pencil must move to draw the letter. The L is completed by connecting the last point in the matrix, (0, 5), to the starting point, (0, 0). Use these ideas to solve Exercises
Describe the determinants Dx and Dy in terms of the coefficients and constants in a system of two equations in two variables.

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