Question

2
\

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

• \

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

a \

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

b not possible
c \

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

d \

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

Explanation:

Step1: Recall Matrix Subtraction Rule

Matrix subtraction is only possible when two matrices have the same dimensions (same number of rows and same number of columns).
The first matrix \(

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

\) has 2 rows and 3 columns (dimension \(2\times3\)).
The second matrix \(

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

\) has 2 rows and 2 columns (dimension \(2\times2\)).

Step2: Check Dimension Compatibility

Since the number of columns in the first matrix (\(3\)) is not equal to the number of columns in the second matrix (\(2\)), matrix subtraction is not possible.

Answer:

B. not possible