Multiply the matrices. (a) $\begin{bmatrix} 3 & 4 & 5 \end{bmatrix} \begin{bmatrix} 6 \ 7 \ 8 \end{bmatrix}$ (b) $\begin{bmatrix} 1 & 2 \end{bmatrix} \begin{bmatrix} 3 & 7 \ 5 & 8 \end{bmatrix}$
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Step 1: To multiply two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix. Show more…
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Use the matrices below to perform matrix multiplication. $$A=\left[\begin{array}{rr} -1 & 5 \\ 3 & 2 \end{array}\right], B=\left[\begin{array}{rrr} 3 & 6 & 4 \\ -8 & 0 & 12 \end{array}\right], C=\left[\begin{array}{rr} 4 & 10 \\ -2 & 6 \\ 5 & 9 \end{array}\right], D=\left[\begin{array}{rrr} 2 & -3 & 12 \\ 9 & 3 & 1 \\ 0 & 8 & -10 \end{array}\right]$$ $$B C$$
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Multiplying two matrices consists of calculating several dot products and then arranging them to form a new matrix. There is a natural way to arrange these dot products, each of which combines a row vector from the first matrix and a column vector from the second matrix. Use the example as a model to calculate the matrix products that follow.
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