Question 1

Solve the system of equations.&#10;

Accepted Answer

The solution to the system of equations is $x_1 = 2$, $x_2 = -7$, and $x_3 = -1$, which matches choice A.

Question 2

Determine whether the system is consistent.&#10;

Accepted Answer

A

Question 3

Determine whether the system is consistent.&#10;

Accepted Answer

B

Question 4

Solve the system of equations.&#10;

Accepted Answer

The correct answer is (0, -6, 1).To solve the system of equations, we can use the method of elimination. First, we can eliminate x3 by adding the first and second equations:5x1 + 2x2 + x3 = -112x1 - 3x2 - x3 = 177x1 - x2 = 6Next, we can eliminate x3 by subtracting the third equation from the first equation:5x1 + 2x2 + x3 = -117x1 + x2 + 2x3 = -4-2x1 - x2 = -7Now we have a system of two equations with two variables:7x1 - x2 = 6-2x1 - x2 = -7We can solve this system by multiplying the second equation by -1 and adding it to the first equation:7x1 - x2 = 62x1 + x2 = 79x1 = 13x1 = 13/9Substituting this value of x1 back into one of the original equations, we can solve for x2:7x1 - x2 = 67(13/9) - x2 = 6x2 = -6Finally, we can solve for x3 by substituting the values of x1 and x2 back into one of the original equations:5x1 + 2x2 + x3 = -115(13/9) + 2(-6) + x3 = -11x3 = 1Therefore, the solution to the system of equations is (0, -6, 1).

Question 5

Solve the system of equations.&#10;

Accepted Answer

Given $x_3 = -4$, substituting this into the second equation gives $4x_2 + 9(-4) = -12$, which simplifies to $4x_2 - 36 = -12$, leading to $4x_2 = 24$, so $x_2 = 6$. Substituting $x_2 = 6$ and $x_3 = -4$ into the first equation gives $x_1 + 3(6) + 2(-4) = 11$, which simplifies to $x_1 + 18 - 8 = 11$, leading to $x_1 = 1$. Therefore, the solution is $(1, 6, -4)$.

Question 6

Solve the system of equations.&#10;

Accepted Answer

The answer of Solve the system of equations.&#10; ...

Question 7

Solve the system of equations.&#10;

Accepted Answer

The answer of Solve the system of equations.&#10; ...

Question 8

Solve the system of equations.&#10;

Accepted Answer

The answer of Solve the system of equations.&#10; ...

Question 9

Solve the system of equations.&#10;

Accepted Answer

The first equation gives $x_1 + x_2 + x_3 = 6$. The second equation gives $x_1 = -2$ and $x_3 = -2$. Substituting these values into the first equation gives $x_2 = 6$. Therefore, the solution to the system of equations is $(x_1, x_2, x_3) = (-2, 6, -2)$.

Question 10

Determine whether the system is consistent.&#10;

Accepted Answer

To determine if the system is consistent, we can check if there is at least one solution to the system of equations. In this case, since the system of equations has three equations and three unknowns (x1, x2, x3), and there is no immediate contradiction from the equations (such as an equation that simplifies to a falsehood like 0=1), the system is likely consistent. Without solving the system explicitly, the presence of three distinct equations for three unknowns typically indicates that the system has at least one solution, assuming the equations are not multiples of each other or do not otherwise reduce to a contradictory statement.

Question 11

Determine whether the system is consistent.&#10;

Accepted Answer

The answer of Determine whether the system is consistent.&#10; ...

Question 12

Determine whether the system is consistent.&#10;

Accepted Answer

The answer of Determine whether the system is consistent.&#10; ...

Question 13

Determine whether the system is consistent.&#10;

Accepted Answer

The answer of Determine whether the system is consistent.&#10; ...

Question 14

Determine whether the system is consistent.&#10;

Accepted Answer

The answer of Determine whether the system is consistent.&#10; ...

Question 15

Solve the system of equations.&#10;

Accepted Answer

The answer of Solve the system of equations.&#10; ...

Question 16

Solve the system of equations.&#10;

Accepted Answer

The answer of Solve the system of equations.&#10; ...

Question 17

Determine whether the system is consistent.&#10;

Accepted Answer

The answer of Determine whether the system is consistent.&#10; ...

Question 18

Determine whether the system is consistent.&#10;

Accepted Answer

The answer of Determine whether the system is consistent.&#10; ...

Question 19

Determine whether the system is consistent.&#10;

Accepted Answer

The answer of Determine whether the system is consistent.&#10; ...

Question 20

Solve the system of equations.&#10;

Accepted Answer

The answer of Solve the system of equations.&#10; ...

Question 21

The augmented matrix is given for a system of equations. If the system is consistent, find the general solution.&#10;Otherwise state that there is no solution.&#10;

Accepted Answer

The answer of The augmented matrix is given for a...

Question 22

The augmented matrix is given for a system of equations. If the system is consistent, find the general solution.&#10;Otherwise state that there is no solution.&#10;

Accepted Answer

The answer of The augmented matrix is given for a...

Question 23

Use the row reduction algorithm to transform the matrix into echelon form or reduced echelon form as indicated.&#10;Find the echelon form of the given matrix.

Accepted Answer

The answer of Use the row reduction algorithm to transform...

Question 24

Determine whether the matrix is in echelon form, reduced echelon form, or neither.&#10; &#10;A)Echelon form&#10;B)Neither&#10;C)Reduced echelon form

Accepted Answer

The answer of Determine whether the matrix is in echelon...

Question 25

Use the row reduction algorithm to transform the matrix into echelon form or reduced echelon form as indicated.&#10;Find the reduced echelon form of the given matrix.

Accepted Answer

The answer of Use the row reduction algorithm to transform...

Question 26

Find the indicated vector.&#10;

Accepted Answer

The answer of Find the indicated vector.&#10; ...

Question 27

The augmented matrix is given for a system of equations. If the system is consistent, find the general solution.&#10;Otherwise state that there is no solution.&#10;

Accepted Answer

The answer of The augmented matrix is given for a...

Question 28

Determine whether the matrix is in echelon form, reduced echelon form, or neither.&#10; &#10;A)Reduced echelon form&#10;B)Echelon form&#10;C)Neither

Accepted Answer

The answer of Determine whether the matrix is in echelon...

Question 29

Determine whether the matrix is in echelon form, reduced echelon form, or neither.&#10; &#10;A)Echelon form&#10;B)Reduced echelon form&#10;C)Neither

Accepted Answer

The answer of Determine whether the matrix is in echelon...

Question 30

The augmented matrix is given for a system of equations. If the system is consistent, find the general solution.&#10;Otherwise state that there is no solution.&#10;

Accepted Answer

The answer of The augmented matrix is given for a...

Question 31

Determine whether the matrix is in echelon form, reduced echelon form, or neither.&#10; &#10;A)Neither&#10;B)Echelon form&#10;C)Reduced echelon form

Accepted Answer

The answer of Determine whether the matrix is in echelon...

Question 32

Determine whether the matrix is in echelon form, reduced echelon form, or neither.&#10; &#10;A)Reduced echelon form&#10;B)Echelon form&#10;C)Neither

Accepted Answer

The answer of Determine whether the matrix is in echelon...

Question 33

The augmented matrix is given for a system of equations. If the system is consistent, find the general solution.&#10;Otherwise state that there is no solution.&#10;

Accepted Answer

The answer of The augmented matrix is given for a...

Question 34

Find the indicated vector.&#10;

Accepted Answer

The answer of Find the indicated vector.&#10; ...

Question 35

Determine whether the matrix is in echelon form, reduced echelon form, or neither.&#10; &#10;A)Neither&#10;B)Echelon form&#10;C)Reduced echelon form

Accepted Answer

The answer of Determine whether the matrix is in echelon...

Question 36

Find the indicated vector.&#10;

Accepted Answer

The answer of Find the indicated vector.&#10; ...

Question 37

Find the indicated vector.&#10;

Accepted Answer

The answer of Find the indicated vector.&#10; ...

Question 38

Determine whether the matrix is in echelon form, reduced echelon form, or neither.&#10; &#10;A)Echelon form&#10;B)Reduced echelon form&#10;C)Neither

Accepted Answer

The answer of Determine whether the matrix is in echelon...

Question 39

The augmented matrix is given for a system of equations. If the system is consistent, find the general solution.&#10;Otherwise state that there is no solution.&#10;

Accepted Answer

The answer of The augmented matrix is given for a...

Question 40

Find the indicated vector.&#10;

Accepted Answer

The answer of Find the indicated vector.&#10; ...

Question 41

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 42

Solve the problem.&#10;Find the general solution of the homogeneous system below. Give your answer as a vector.

Accepted Answer

The answer of Solve the problem.&#10;Find the general solution of...

Question 43

Compute the product or state that it is undefined.&#10;

Accepted Answer

The answer of Compute the product or state that it...

Question 44

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 45

Solve the problem.&#10;A company manufactures two products. For $1.00 worth of product A, the company &#10;spends $0.40 on materials, $0.25 on labor, and $0.10 on overhead. For $1.00 worth of&#10;product B, the company spends $0.50 on materials, $0.20 on labor, and $0.10 on overhead.&#10;Let   Then a and b represent the &#698;costs per dollar of income&#698; for the two products.&#10;Evaluate 100a + 400b and give an economic interpretation of the result.

Accepted Answer

The answer of Solve the problem.&#10;A company manufactures two products....

Question 46

Display the indicated vector(s) on an xy-graph.&#10;

Accepted Answer

The answer of Display the indicated vector(s) on an xy-graph.&#10;...

Question 47

Find the indicated vector.&#10;

Accepted Answer

The answer of Find the indicated vector.&#10; ...

Question 48

Find the indicated vector.&#10;

Accepted Answer

The answer of Find the indicated vector.&#10; ...

Question 49

Find the indicated vector.&#10;

Accepted Answer

The answer of Find the indicated vector.&#10; ...

Question 50

Write the system as a vector equation or matrix equation as indicated.
Write the following system as a matrix equation involving the product of a matrix and a vector on the left side and a vector on the right side.

Accepted Answer

The answer of Write the system as a vector equation...

Question 51

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 52

Compute the product or state that it is undefined.&#10;

Accepted Answer

The answer of Compute the product or state that it...

Question 53

Compute the product or state that it is undefined.&#10;

Accepted Answer

The answer of Compute the product or state that it...

Question 54

Solve the problem.&#10;Describe all solutions of Ax = b, where

Accepted Answer

The answer of Solve the problem.&#10;Describe all solutions of Ax...

Question 55

Solve the problem.&#10;A company manufactures two products. For $1.00 worth of product A, the company &#10;spends $0.50 on materials, $0.20 on labor, and $0.15 on overhead. For $1.00 worth of&#10;product B, the company spends $0.45 on materials, $0.20 on labor, and $0.15 on overhead.&#10;Let

Accepted Answer

The answer of Solve the problem.&#10;A company manufactures two products....

Question 56

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10;   ...

Question 57

Write the system as a vector equation or matrix equation as indicated.&#10;Write the following system as a vector equation involving a linear combination of vectors.