Matrix Addition Example
Question:
Compute the sum: \[ \begin{bmatrix} 3 & -2 \\ 1 & 4 \end{bmatrix} + \begin{bmatrix} -2 & 4 \\ 1 & 3 \end{bmatrix} \]
Compute the sum: \[ \begin{bmatrix} 3 & -2 \\ 1 & 4 \end{bmatrix} + \begin{bmatrix} -2 & 4 \\ 1 & 3 \end{bmatrix} \]
Solution:
Matrix addition is done by adding corresponding elements.
\[ = \begin{bmatrix} 3 + (-2) & -2 + 4 \\ 1 + 1 & 4 + 3 \end{bmatrix} \] \[ = \begin{bmatrix} 1 & 2 \\ 2 & 7 \end{bmatrix} \]Final Answer:
\[ \boxed{ \begin{bmatrix} 1 & 2 \\ 2 & 7 \end{bmatrix} } \]