If \(A = \begin{bmatrix} \frac{2}{3} & 1 & \frac 53 \\[0.3em] \frac{1}{3} & \frac 23 & \frac{4}{3} \\[0.3em] \frac 73 & 2 & \frac{2}{3} \end{bmatrix}\) and \(B = \begin{bmatrix} \frac{2}{5} & \frac 35 & 1 \\[0.3em] \frac{1}{5} & \frac 25 & \frac{4}{5} \\[0.3em] \frac 75 & \frac 65 & \frac{2}{5} \end{bmatrix}\) then compute 3A-5B.
If \(A = \begin{bmatrix} \frac{2}{3} & 1 & \frac 53 \\[0.3em] \frac{1}{3} & \frac 23 & \frac{4}{3} \\[0.3em] \frac 73 & 2 & \frac{2}{3} \end{bmatrix}\) and \(B = \begin{bmatrix} \frac{2}{5} & \frac 35 & 1 \\[0.3em] \frac{1}{5} & \frac 25 & \frac{4}{5} \\[0.3em] \frac 75 & \frac 65 & \frac{2}{5} \end{bmatrix}\) then compute 3A-5B.
Solution and Explanation
3A - 5B = 3\(\begin{bmatrix} \frac{2}{3} & 1 & \frac 53 \\[0.3em] \frac{1}{3} & \frac 23 & \frac{4}{3} \\[0.3em] \frac 73 & 2 & \frac{2}{3} \end{bmatrix}\)- 5 \(\begin{bmatrix} \frac{2}{5} & \frac 35 & 1 \\[0.3em] \frac{1}{5} & \frac 25 & \frac{4}{5} \\[0.3em] \frac 75 & \frac 65 & \frac{2}{5} \end{bmatrix}\)
= \(\begin{bmatrix} 2 & 3 & 5 \\[0.3em] 1 & 2 & 4 \\[0.3em] 7 & 6 & 2 \end{bmatrix}\)- \(\begin{bmatrix} 2 & 3 & 5 \\[0.3em] 1 & 2 & 4 \\[0.3em] 7 & 6 & 2 \end{bmatrix}\)
= \(\begin{bmatrix} 0 & 0 & 0 \\[0.3em] 0 & 0 & 0 \\[0.3em] 0 & 0 & 0 \end{bmatrix}\)
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