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

Question

If $A =\left[\begin{array}{rr}8 & 0 \\ 4 & -2 \\ 3 & 6\end{array}\right], B =\left[\begin{array}{rr}2 & -2 \\ 4 & 2 \\ -5 & 1\end{array}\right]$ and $2 A+3 x=5 B$ then find the value of $x$.

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Answer

Rearrange the equation for $X: 3 X=5 B-2 A$.
Calculate $5 B: 5\left[\begin{array}{cc}2 & -2 \\ 4 & 2 \\ -5 & 1\end{array}\right]=\left[\begin{array}{cc}10 & -10 \\ 20 & 10 \\ -25 & 5\end{array}\right]$.
Calculate $2 A: 2\left[\begin{array}{cc}8 & 0 \\ 4 & -2 \\ 3 & 6\end{array}\right]=\left[\begin{array}{cc}16 & 0 \\ 8 & -4 \\ 6 & 12\end{array}\right]$.
Subtract: $3 X=\left[\begin{array}{cc}10-16 & -10-0 \\ 20-8 & 10-(-4) \\ -25-6 & 5-12\end{array}\right]=\left[\begin{array}{cc}-6 & -10 \\ 12 & 14 \\ -31 & -7\end{array}\right]$
$X=$ $\frac{1}{3}\left[\begin{array}{cc}-6 & -10 \\ 12 & 14 \\ -31 & -7\end{array}\right]$.

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