Find Matrix A
Given:
\[ A + \begin{bmatrix} 2 & 3 \\ -1 & 4 \end{bmatrix} = \begin{bmatrix} 3 & -6 \\ -3 & 8 \end{bmatrix} \]
Step 1: Rearrange
\[ A = \begin{bmatrix} 3 & -6 \\ -3 & 8 \end{bmatrix} – \begin{bmatrix} 2 & 3 \\ -1 & 4 \end{bmatrix} \]
Step 2: Subtract Elements
\[ A = \begin{bmatrix} 3 – 2 & -6 – 3 \\ -3 – (-1) & 8 – 4 \end{bmatrix} \]
\[ A = \begin{bmatrix} 1 & -9 \\ -2 & 4 \end{bmatrix} \]
Final Answer:
\[ A = \begin{bmatrix} 1 & -9 \\ -2 & 4 \end{bmatrix} \]