If A= [ cc 8 & 0 4 & -2 3 & 6 ] and B= [ cc 2 & -2 4 & 2 -5 & 1 ]… - Vidyadip

Question

If $A=\left[\begin{array}{cc}8 & 0 \\ 4 & -2 \\ 3 & 6\end{array}\right]$ and $B=\left[\begin{array}{cc}2 & -2 \\ 4 & 2 \\ -5 & 1\end{array}\right]$, then find the matrix $X$ such that $2 A+3 X=5 B$.

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Answer

Given:3X = 5B - 2A
$=5\left[ {\begin{array}{*{20}{c}} 2 \\ 4 \\ { - 5} \end{array}\;\;\begin{array}{*{20}{c}} { - 2} \\ 2 \\ 1 \end{array}} \right] - 2\left[ {\begin{array}{*{20}{c}} 8 \\ 4 \\ 3 \end{array}\;\;\begin{array}{*{20}{c}} 0 \\ { - 2} \\ 6 \end{array}} \right]$
$ = \left[ {\begin{array}{*{20}{c}} {10} \\ {20} \\ { - 25} \end{array}\;\;\begin{array}{*{20}{c}} { - 10} \\ {10} \\ 5 \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} { - 16} \\ { - 8} \\ { - 6} \end{array}\;\;\begin{array}{*{20}{c}} 0 \\ 4 \\ { - 12} \end{array}} \right]$
$ = \left[ {\begin{array}{*{20}{c}} { - 6} \\ {12} \\ { - 31} \end{array}\;\;\begin{array}{*{20}{c}} { - 10} \\ {14} \\ { - 7} \end{array}} \right]$
$X = \frac{1}{3}\left[ {\begin{array}{*{20}{c}} { - 6} \\ {12} \\ { - 31} \end{array}\;\;\begin{array}{*{20}{c}} { - 10} \\ {14} \\ { - 7} \end{array}} \right]$

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