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

Question

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

3A – 4B + 5X = C.

✓

Answer

3A-4B + 5X = C ∴ 5X = C + 4B – 3A

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

$=\left[\begin{array}{cc}2 & 4 \\ -1 & -4 \\ -3 & 6\end{array}\right]+\left[\begin{array}{cc}-4 & -8 \\ 16 & 8 \\ 4 & 20\end{array}\right]-\left[\begin{array}{cc}3 & -6 \\ 9 & -15 \\ -18 & 0\end{array}\right]$

$=\left[\begin{array}{cc}2-4-3 & 4-8+6 \\ -1+16-9 & -4+8+15 \\ -3+4+18 & 6+20-0\end{array}\right]$

$\therefore \quad 5 X=\left[\begin{array}{cc}-5 & 2 \\ 6 & 19 \\ 19 & 26\end{array}\right]$

$\therefore \quad X=\frac{1}{5}\left[\begin{array}{cc}-5 & 2 \\ 6 & 19 \\ 19 & 26\end{array}\right]=\left[\begin{array}{cc}-1 & \frac{2}{5} \\ \frac{6}{5} & \frac{19}{5} \\ \frac{19}{5} & \frac{26}{5}\end{array}\right]$

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