Given two matrices \(A = \begin{pmatrix} 2 & 3 \\ 4 & 5 \\ 6 & 7 \end{pmatrix}\) and \(B = \begin{pmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{pmatrix}\), find the sum \(A + B\).
Answer
Finally, we simplify the expressions to obtain the final sum: \[A + B = \begin{pmatrix} 3 & 5 \\ 7 & 9 \\ 11 & 13 \end{pmatrix}\]
Step 1 ：First, we align the matrices \(A\) and \(B\) such that corresponding elements are in the same position. This gives us: \[A = \begin{pmatrix} 2 & 3 \\ 4 & 5 \\ 6 & 7 \end{pmatrix}, B = \begin{pmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{pmatrix}\]
Step 2 ：Next, we add corresponding elements from the two matrices to find the sum. This gives us: \[A + B = \begin{pmatrix} 2+1 & 3+2 \\ 4+3 & 5+4 \\ 6+5 & 7+6 \end{pmatrix}\]
Step 3 ：Finally, we simplify the expressions to obtain the final sum: \[A + B = \begin{pmatrix} 3 & 5 \\ 7 & 9 \\ 11 & 13 \end{pmatrix}\]
