Example Question - multiplying matrices

Matrix Multiplication and Addition Exercise

To solve this problem, we need to multiply matrix A by 2 and then add the resulting matrix to matrix B. We'll multiply each entry of matrix A by 2 and then add the corresponding entries of matrix B to these results. Matrix A: \[ \begin{pmatrix} 5 & 1 \\ 2 & 3 \\ 1 & 4 \end{pmatrix} \] Matrix B: \[ \begin{pmatrix} 2 & 4 \\ 1 & -3 \\ 2 & -1 \end{pmatrix} \] Step 1: Multiply each entry of matrix A by 2: \[ 2 \times A = 2 \times \begin{pmatrix} 5 & 1 \\ 2 & 3 \\ 1 & 4 \end{pmatrix} = \begin{pmatrix} 2 \times 5 & 2 \times 1 \\ 2 \times 2 & 2 \times 3 \\ 2 \times 1 & 2 \times 4 \end{pmatrix} = \begin{pmatrix} 10 & 2 \\ 4 & 6 \\ 2 & 8 \end{pmatrix} \] Step 2: Add matrices 2A and B: \[ 2A + B = \begin{pmatrix} 10 & 2 \\ 4 & 6 \\ 2 & 8 \end{pmatrix} + \begin{pmatrix} 2 & 4 \\ 1 & -3 \\ 2 & -1 \end{pmatrix} = \begin{pmatrix} 10+2 & 2+4 \\ 4+1 & 6-3 \\ 2+2 & 8-1 \end{pmatrix} = \begin{pmatrix} 12 & 6 \\ 5 & 3 \\ 4 & 7 \end{pmatrix} \] The resulting matrix is: \[ \begin{pmatrix} 12 & 6 \\ 5 & 3 \\ 4 & 7 \end{pmatrix} \] By comparing this result with the options provided, we can see that the answer is option C.