Finding Matrix A
Question:
If \[ \begin{bmatrix} 1 & 2 & -1 \\ 0 & 4 & 9 \end{bmatrix} + A = \begin{bmatrix} 9 & -1 & 4 \\ -2 & 1 & 3 \end{bmatrix} \] find matrix \(A\).
If \[ \begin{bmatrix} 1 & 2 & -1 \\ 0 & 4 & 9 \end{bmatrix} + A = \begin{bmatrix} 9 & -1 & 4 \\ -2 & 1 & 3 \end{bmatrix} \] find matrix \(A\).
Solution:
Step 1: Rearrange the equation
\[ A = \begin{bmatrix} 9 & -1 & 4 \\ -2 & 1 & 3 \end{bmatrix} – \begin{bmatrix} 1 & 2 & -1 \\ 0 & 4 & 9 \end{bmatrix} \]Step 2: Subtract corresponding elements
\[ A = \begin{bmatrix} 9-1 & -1-2 & 4-(-1) \\ -2-0 & 1-4 & 3-9 \end{bmatrix} = \begin{bmatrix} 8 & -3 & 5 \\ -2 & -3 & -6 \end{bmatrix} \]Final Answer:
\[ \boxed{ \begin{bmatrix} 8 & -3 & 5 \\ -2 & -3 & -6 \end{bmatrix} } \]