If \( A = \begin{bmatrix} 2 & 3\\ 4 & 5 \end{bmatrix} \), find the result of the scalar multiplication \( 3A \).
Answer
Finally, simplify the resulting matrix. \( \begin{bmatrix} 3 \times 2 & 3 \times 3\\ 3 \times 4 & 3 \times 5 \end{bmatrix} = \begin{bmatrix} 6 & 9\\ 12 & 15 \end{bmatrix} \).
Step 1 ：First, identify the scalar and the matrix. The scalar is 3 and the matrix is \( A = \begin{bmatrix} 2 & 3\\ 4 & 5 \end{bmatrix} \).
Step 2 ：Second, multiply each element in the matrix by the scalar. \( 3 \times \begin{bmatrix} 2 & 3\\ 4 & 5 \end{bmatrix} = \begin{bmatrix} 3 \times 2 & 3 \times 3\\ 3 \times 4 & 3 \times 5 \end{bmatrix} \).
Step 3 ：Finally, simplify the resulting matrix. \( \begin{bmatrix} 3 \times 2 & 3 \times 3\\ 3 \times 4 & 3 \times 5 \end{bmatrix} = \begin{bmatrix} 6 & 9\\ 12 & 15 \end{bmatrix} \).
