If A - begin bmatrix -frac 23- 1 - frac 53 frac 73- 2 - frac 23 llendbmatrix B - beginbmatrix -frac 23-frac35- 1 lendbmatrix then compute 3 A -5 B

A=[ 2/3 amp; 1 amp; 5/3; 1/3 amp; 2/3 amp; 4/3; 7/3 amp; 2 amp; 2/3; ] B=[ 2/3 amp; 3/5 amp;1; 1/5 amp;2/5 amp;4/5; ...

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Quantitative Aptitude

Permutation

If A = begin ...

Question

If $A = ⎡ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{2}{3} & 1 & \frac{5}{3} \frac{1}{3} & \frac{2}{3} & \frac{4}{3} \frac{7}{3} & 2 & \frac{2}{3} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎦ B = ⎡ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{2}{3} & \frac{3}{5} & 1 \frac{1}{5} & \frac{2}{5} & \frac{4}{5} \frac{7}{5} & \frac{6}{5} & \frac{2}{5} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎦$ then compute 3A-5B

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Solution

$A = ⎡ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{2}{3} & 1 & \frac{5}{3} \frac{1}{3} & \frac{2}{3} & \frac{4}{3} \frac{7}{3} & 2 & \frac{2}{3} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎦ B = ⎡ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{2}{3} & \frac{3}{5} & 1 \frac{1}{5} & \frac{2}{5} & \frac{4}{5} \frac{7}{5} & \frac{6}{5} & \frac{2}{5} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎦$
$3 A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 3 & 5 1 & 2 & 4 7 & 6 & 2 \end{matrix} ⎤ ⎥ ⎦ B = ⎡ ⎢ ⎣ \begin{matrix} 2 & 3 & 5 1 & 2 & 4 7 & 6 & 2 \end{matrix} ⎤ ⎥ ⎦$
So, $3 A - 3 B = ⎡ ⎢ ⎣ \begin{matrix} 2 & 3 & 5 1 & 2 & 4 7 & 6 & 2 \end{matrix} ⎤ ⎥ ⎦ - ⎡ ⎢ ⎣ \begin{matrix} 2 & 3 & 5 1 & 2 & 4 7 & 6 & 2 \end{matrix} ⎤ ⎥ ⎦$
$⎡ ⎢ ⎣ \begin{matrix} 0 & 0 & 0 0 & 0 & 0 0 & 0 & 0 \end{matrix} ⎤ ⎥ ⎦$

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If $A = ⎡ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{2}{3} & 1 & \frac{5}{3} \frac{1}{3} & \frac{2}{3} & \frac{4}{3} \frac{7}{3} & 2 & \frac{2}{3} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎦ a n d B = ⎡ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{2}{5} & \frac{3}{5} & 1 \frac{1}{5} & \frac{2}{5} & \frac{4}{5} \frac{7}{5} & \frac{6}{5} & \frac{2}{5} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎦$ , then compute 3A -5B.