Question

perform the following operations (if possible)
$a = \

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

$ $b = \

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

$ $c = \

$$\begin{bmatrix} -3 & 1 \\\\ 5 & -2 \\\\ 0 & 1 \\end{bmatrix}$$

$

1. $a + b$
2. $a - b$
3. $b - a$
4. $c + b$

Explanation:

7. \( A + B \)

Step1: Check matrix dimensions

Matrix \( A \) is \( 2 \times 3 \), matrix \( B \) is \( 2 \times 3 \). Same dimensions, so addition is possible.

Step2: Add corresponding elements

For element \((1,1)\): \( 0 + 4 = 4 \)
For element \((1,2)\): \( 7 + 2 = 9 \) (Wait, \( B \) has \(-2\)? Wait, \( B =

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

\), \( A =

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

\)
So \( A + B =

$$\begin{bmatrix}0 + 4 & 7 + (-2) & 3 + 1 \\ -2 + 1 & 3 + (-3) & 0 + 6\end{bmatrix}$$

\)

Step3: Calculate each element

\( (1,1): 4 \), \( (1,2): 7 - 2 = 5 \), \( (1,3): 3 + 1 = 4 \)
\( (2,1): -2 + 1 = -1 \), \( (2,2): 3 - 3 = 0 \), \( (2,3): 0 + 6 = 6 \)
So \( A + B =

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

\)

Step1: Check matrix dimensions

\( B \) and \( A \) are both \( 2 \times 3 \), so subtraction is possible.

Step2: Subtract corresponding elements

\( B - A =

$$\begin{bmatrix}4 - 0 & -2 - 7 & 1 - 3 \\ 1 - (-2) & -3 - 3 & 6 - 0\end{bmatrix}$$

\)

Step3: Calculate each element

\( (1,1): 4 \), \( (1,2): -2 - 7 = -9 \), \( (1,3): 1 - 3 = -2 \)
\( (2,1): 1 + 2 = 3 \), \( (2,2): -3 - 3 = -6 \), \( (2,3): 6 \)
So \( B - A =

$$\begin{bmatrix}4 & -9 & -2 \\ 3 & -6 & 6\end{bmatrix}$$

\)

Step1: Check matrix dimensions

\( A \) and \( B \) are both \( 2 \times 3 \), so subtraction is possible.

Step2: Subtract corresponding elements

\( A - B =

$$\begin{bmatrix}0 - 4 & 7 - (-2) & 3 - 1 \\ -2 - 1 & 3 - (-3) & 0 - 6\end{bmatrix}$$

\)

Step3: Calculate each element

\( (1,1): -4 \), \( (1,2): 7 + 2 = 9 \), \( (1,3): 2 \)
\( (2,1): -3 \), \( (2,2): 3 + 3 = 6 \), \( (2,3): -6 \)
So \( A - B =

$$\begin{bmatrix}-4 & 9 & 2 \\ -3 & 6 & -6\end{bmatrix}$$

\)

Answer:

\(

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

\)

8. \( B - A \)