Question

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

Answer 1

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

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