Question

If \( A = \begin{pmatrix} -2 & 3 \\ 1 & 2 \end{pmatrix} \) and \( B = \begin{pmatrix} -1 & 0 \\ 1 & 2 \end{pmatrix} \), then find \( (A + B) \).

Hint:

When adding matrices, simply add the corresponding elements from each matrix.

Answer 1

Step 1: Matrix addition. 

To find \( A + B \), we add the corresponding elements of matrices \( A \) and \( B \): \[ A + B = \begin{pmatrix} -2 & 3 \\ 1 & 2 \end{pmatrix} + \begin{pmatrix} -1 & 0 \\ 1 & 2 \end{pmatrix} = \begin{pmatrix} -2 + (-1) & 3 + 0 \\ 1 + 1 & 2 + 2 \end{pmatrix} \] \[ A + B = \begin{pmatrix} -3 & 3 \\ 2 & 4 \end{pmatrix} \]

Step 2: Conclusion. 

Thus, the sum \( A + B \) is: \[ A + B = \begin{pmatrix} -3 & 3 \\ 2 & 4 \end{pmatrix} \]