Question - Matrix Multiplication and Addition Exercise
Solution:
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.
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