Matrix Addition (3×3) Example
Question:
Compute: \[ \begin{bmatrix} 2 & 1 & 3 \\ 0 & 3 & 5 \\ -1 & 2 & 5 \end{bmatrix} + \begin{bmatrix} 1 & -2 & 3 \\ 2 & 6 & 1 \\ 0 & -3 & 1 \end{bmatrix} \]
Compute: \[ \begin{bmatrix} 2 & 1 & 3 \\ 0 & 3 & 5 \\ -1 & 2 & 5 \end{bmatrix} + \begin{bmatrix} 1 & -2 & 3 \\ 2 & 6 & 1 \\ 0 & -3 & 1 \end{bmatrix} \]
Solution:
Add corresponding elements of the matrices:
\[ = \begin{bmatrix} 2+1 & 1+(-2) & 3+3 \\ 0+2 & 3+6 & 5+1 \\ -1+0 & 2+(-3) & 5+1 \end{bmatrix} \] \[ = \begin{bmatrix} 3 & -1 & 6 \\ 2 & 9 & 6 \\ -1 & -1 & 6 \end{bmatrix} \]Final Answer:
\[ \boxed{ \begin{bmatrix} 3 & -1 & 6 \\ 2 & 9 & 6 \\ -1 & -1 & 6 \end{bmatrix} } \]