Blitzer - College Algebra 8th Edition

Ch. 6 - Matrices and Determinants

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Blitzer 8th Edition

Ch. 6 - Matrices and Determinants

Problem 9a

In Exercises 9 - 16, find the following matrices: a. A + B

Problem 9b

In Exercises 9 - 16, find the following matrices: b. A - B

Problem 9c

In Exercises 9 - 16, find the following matrices: c. - 4A

Problem 9d

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B

Problem 10

In Exercises 8–11, use Gaussian elimination to find the complete solution to each system, or show that none exists.

Problem 11

For Exercises 11–22, use Cramer's Rule to solve each system. $\begin{cases} x + y = 7 \\ x - y = 3 \end{cases}$

Problem 11

Find the products AB and BA to determine whether B is the multiplicative inverse of A.

$A = [\begin{matrix} 0 & 0 & - 2 & 1 \\ - 1 & 0 & 1 & 1 \\ 0 & 1 & - 1 & 0 \\ 1 & 0 & 0 & - 1 \end{matrix}],$

Problem 11

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.

$\begin{bmatrix} 1 & 1 & 4 & 1 & \vert & 3 \\ -1 & 1 & -1 & 0 & \vert & 7 \\ 2 & 0 & 0 & 5 & \vert & 11 \\ 0 & 0 & 12 & 4 & \vert & 5 \end{bmatrix}$

Problem 11

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases} 2w + x - y = 3 \\ w - 3x + 2y = -4 \\ 3w + x - 3y + z = 1 \\ w + 2x - 4y - z = -2 \end{cases}$

Problem 11a

In Exercises 9 - 16, find the following matrices: a. A + B

Problem 11b

In Exercises 9 - 16, find the following matrices: b. A - B

Problem 11c

In Exercises 9 - 16, find the following matrices: c. - 4A

Problem 11d

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B

Problem 12a

In Exercises 9 - 16, find the following matrices: a. A + B

Problem 12b

In Exercises 9 - 16, find the following matrices: b. A - B

Problem 12c

In Exercises 9 - 16, find the following matrices: c. - 4A

Problem 12d

Find the following matrices: - 3A + 2B

$A = \begin{bmatrix} 3 & 1 & 1 \\ -1 & 2 & 5 \end{bmatrix} , B = \begin{bmatrix} 2 & -3 & 6 \\ -3 & 1 & -4 \end{bmatrix}$

Problem 13

Perform each matrix row operation and write the new matrix.

$\begin{bmatrix} 2 & -6 & 4 & \vert & 10 \\ 1 & 5 & -5 & \vert & 0 \\ 3 & 0 & 4 & \vert & 7 \end{bmatrix} \quad \frac{1}{2}R_1$

Problem 13

Use the fact that if $A = [\begin{matrix} a & b \\ c & d \end{matrix}]$ , then $A^{- 1} = \frac{1}{a d - b c} [\begin{matrix} d & - b \\ - c & a \end{matrix}]$ to find the inverse of each matrix, if possible. Check that $A A^{- 1} = I_{2}$ and $A^{- 1} A = I_{2}$ .

$A = [\begin{matrix} 2 & 3 \\ - 1 & 2 \end{matrix}]$

Problem 13

For Exercises 11–22, use Cramer's Rule to solve each system. $\begin{cases} 12x + 3y = 15 \\ 2x - 3y = 13 \end{cases}$

Problem 13

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases} w - 3x + y - 4z = 4 \\ -2w + x + 2y = -2 \\ 3w - 2x + y - 6z = 2 \\ -w + 3x + 2y - z = -6 \end{cases}$