If A= [ ccc 2 3 & 1 & 5 3 1 3 & 2 3 & 4 3 7 3 & 2 & 2 3 ] and B= … - Vidyadip

Question

If $A=\left[\begin{array}{ccc}\frac{2}{3} & 1 & \frac{5}{3} \\ \frac{1}{3} & \frac{2}{3} & \frac{4}{3} \\ \frac{7}{3} & 2 & \frac{2}{3}\end{array}\right]$ and $B=\left[\begin{array}{ccc}\frac{2}{5} & \frac{3}{5} & 1 \\ \frac{1}{5} & \frac{2}{5} & \frac{4}{5} \\ \frac{7}{5} & \frac{6}{5} & \frac{2}{5}\end{array}\right]$, then compute $3 A-5 B$.

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Answer

3A – 5B = $3\left[ {\begin{array}{*{20}{c}} {\frac{2}{3}}&1&{\frac{5}{3}} \\ {\frac{1}{3}}&{\frac{2}{3}}&{\frac{4}{3}} \\ {\frac{7}{3}}&2&{\frac{2}{3}} \end{array}} \right] - 5\left[ {\begin{array}{*{20}{c}} {\frac{2}{5}}&{\frac{3}{5}}&1 \\ {\frac{1}{5}}&{\frac{2}{5}}&{\frac{4}{5}} \\ {\frac{7}{5}}&{\frac{6}{5}}&{\frac{2}{5}} \end{array}} \right]$

$ = \left[ {\begin{array}{*{20}{c}} 2&3&5 \\ 1&2&4 \\ 7&6&2 \end{array}} \right] - \left[ {\begin{array}{*{20}{c}} 2&3&5 \\ 1&2&4 \\ 7&6&2 \end{array}} \right]$
$ = \left[ {\begin{array}{*{20}{c}} {2 - 2}&{3 - 3}&{5 - 5} \\ {1 - 1}&{2 - 2}&{4 - 4} \\ {7 - 7}&{6 - 6}&{2 - 2} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 0&0&0 \\ 0&0&0 \\ 0&0&0 \end{array}} \right]$

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