Question

if $x = \

$$\begin{bmatrix} -1 & 6 & 7 \\\\ 9 & -4 & 2 \\end{bmatrix}$$

$ and $y = \

$$\begin{bmatrix} 6 & -1 & -2 \\\\ -4 & 3 & -1 \\end{bmatrix}$$

$, what is $x - y$?
if the matrix exists, select its size before entering your answer. if the matrix does not exist, select undefined.
$x - y = \

$$\begin{bmatrix}\\square\\end{bmatrix}$$

$
\boxed{\

$$\begin{array}{|c|c|c|} \\hline 1\\times1 & 1\\times2 & 1\\times3 & 1\\times4 \\\\ \\hline 2\\times1 & 2\\times2 & 2\\times3 & 2\\times4 \\\\ \\hline 3\\times1 & 3\\times2 & 3\\times3 & 3\\times4 \\\\ \\hline 4\\times1 & 4\\times2 & 4\\times3 & 4\\times4 \\\\ \\hline \\text{undefined} \\\\ \\hline \\end{array}$$

}

Explanation:

Step1: Check matrix dimensions

Both \( X \) and \( Y \) are \( 2 \times 3 \) matrices (2 rows, 3 columns), so subtraction is defined.

Step2: Subtract corresponding elements

For the first row, first column: \( -1 - 6 = -7 \)
First row, second column: \( 6 - (-1) = 7 \)
First row, third column: \( 7 - (-2) = 9 \)
Second row, first column: \( 9 - (-4) = 13 \)
Second row, second column: \( -4 - 3 = -7 \)
Second row, third column: \( 2 - (-1) = 3 \)

Answer:

The size is \( 2 \times 3 \), and \( X - Y =

$$\begin{bmatrix} -7 & 7 & 9 \\ 13 & -7 & 3 \end{bmatrix}$$

\)