Question

use matrices a, b, and c. find the sum or difference if you can.
$a = \

$$\begin{bmatrix} -5 & 4 \\\\ -8 & 2 \\end{bmatrix}$$

$ $b = \

$$\begin{bmatrix} -2 & 7 & -3 \\\\ 1 & -6 & 0 \\end{bmatrix}$$

$ $c = \

$$\begin{bmatrix} 5 & 3 & -1 \\\\ -3 & 0 & 6 \\end{bmatrix}$$

$

1. $b - a$

a. $\

$$\begin{bmatrix} -7 & -4 & 2 \\\\ -4 & 6 & 6 \\end{bmatrix}$$

$
b. not possible
c. $\

$$\begin{bmatrix} -7 & 11 \\\\ -7 & -4 \\end{bmatrix}$$

$
d. $\

$$\begin{bmatrix} 3 & 10 & -4 \\\\ -2 & -6 & 6 \\end{bmatrix}$$

$
determine whether the product is defined or undefined. if defined, give the dimensions of the product matrix.

1. $\

$$\begin{bmatrix} 1 & 1 & -4 \\\\ 5 & 6 & 0 \\end{bmatrix}$$

\

$$\begin{bmatrix} 9 \\\\ 1 \\\\ -7 \\end{bmatrix}$$

$
a. defined; $3 \times 3$
b. defined; $2 \times 1$
c. defined; $2 \times 3$
d. undefined

1. (partially visible matrix multiplication problem)

a. (partially visible)
b. (partially visible)
c. defined; $1 \times 2$
d. undefined

Explanation:

Question 98:

Step1: Check matrix dimensions

Matrix \( A \) is \( 2 \times 2 \) (2 rows, 2 columns), matrix \( B \) is \( 2 \times 3 \) (2 rows, 3 columns). For matrix subtraction \( B - A \), the matrices must have the same dimensions (same number of rows and columns). Since \( A \) and \( B \) have different column counts (2 vs. 3), subtraction is not possible.

Step1: Recall matrix multiplication rule

For matrix multiplication, the number of columns in the first matrix must equal the number of rows in the second matrix. The first matrix is \( 2 \times 3 \) (2 rows, 3 columns), the second matrix is \( 3 \times 1 \) (3 rows, 1 column). Since \( 3 = 3 \), the product is defined.

Step2: Determine product dimensions

The product matrix will have the number of rows of the first matrix and the number of columns of the second matrix. So, \( 2 \) rows (from first matrix) and \( 1 \) column (from second matrix), giving dimensions \( 2 \times 1 \).

Step1: Check matrix multiplication rule

For matrix multiplication, the number of columns in the first matrix must equal the number of rows in the second matrix. The first matrix (let's say) is \( 2 \times 2 \) (2 columns), the second matrix is \( 1 \times 2 \) (1 row). Since \( 2
eq 1 \), the product is undefined.

Answer:

b. not possible

Question 99: