If A = begin{bmatrix} frac{2}{3} & 1 & frac{5 | vedclass

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(A) Given $A = \begin{bmatrix} \frac{2}{3} & 1 & \frac{5}{3} \ \frac{1}{3} & \frac{2}{3} & \frac{4}{3} \ \frac{7}{3} & 2 & \frac{2}{3} \end{bmatrix}

Vedclass · Accepted Answer

$\begin{bmatrix} 0 & 0 & 0 \ 0 & 0 & 0 \ 0 & 0 & 0 \end{bmatrix}$

Vedclass · Answer

(A) Given $A = \begin{bmatrix} \frac{2}{3} & 1 & \frac{5}{3} \ \frac{1}{3} & \frac{2}{3} & \frac{4}{3} \ \frac{7}{3} & 2 & \frac{2}{3} \end{bmatrix}$ and $B = \begin{bmatrix} \frac{2}{5} & \frac{3}{5} & 1 \ \frac{1}{5} & \frac{2}{5} & \frac{4}{5} \ \frac{7}{5} & \frac{6}{5} & \frac{2}{5} \end{bmatrix}$.First,calculate $3A$:$3A = 3 	imes \begin{bmatrix} \frac{2}{3} & 1 & \frac{5}{3} \ \frac{1}{3} & \frac{2}{3} & \frac{4}{3} \ \frac{7}{3} & 2 & \frac{2}{3} \end{bmatrix} = \begin{bmatrix} 2 & 3 & 5 \ 1 & 2 & 4 \ 7 & 6 & 2 \end{bmatrix}$.Next,calculate $5B$:$5B = 5 	imes \begin{bmatrix} \frac{2}{5} & \frac{3}{5} & 1 \ \frac{1}{5} & \frac{2}{5} & \frac{4}{5} \ \frac{7}{5} & \frac{6}{5} & \frac{2}{5} \end{bmatrix} = \begin{bmatrix} 2 & 3 & 5 \ 1 & 2 & 4 \ 7 & 6 & 2 \end{bmatrix}$.Finally,compute $3A - 5B$:$3A - 5B = \begin{bmatrix} 2 & 3 & 5 \ 1 & 2 & 4 \ 7 & 6 & 2 \end{bmatrix} - \begin{bmatrix} 2 & 3 & 5 \ 1 & 2 & 4 \ 7 & 6 & 2 \end{bmatrix} = \begin{bmatrix} 0 & 0 & 0 \ 0 & 0 & 0 \ 0 & 0 & 0 \end{bmatrix}$.

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