Question

let a = \\(\

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

\\) and b = \\(\

$$\begin{bmatrix} -2 & -3 \\\\ 5 & 3 \\end{bmatrix}$$

\\). find b - a, if possible.

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

\\(\bigcirc\\) a. b - a = \\(\square\\)
(type an integer or simplified fraction for each matrix element.)
\\(\bigcirc\\) b. b - a is undefined.

Explanation:

Step1: Check Matrix Dimensions

Both matrices \( A \) and \( B \) are \( 2 \times 2 \) (2 rows, 2 columns), so subtraction is possible.

Step2: Subtract Corresponding Elements

For element \((1,1)\): \( B_{1,1}-A_{1,1} = -2 - (-3) = -2 + 3 = 1 \)
For element \((1,2)\): \( B_{1,2}-A_{1,2} = -3 - 2 = -5 \)
For element \((2,1)\): \( B_{2,1}-A_{2,1} = 5 - 2 = 3 \)
For element \((2,2)\): \( B_{2,2}-A_{2,2} = 3 - 0 = 3 \)

Answer:

A. \( B - A =

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

\)