If A= [ cc 1 & -2 3 & -5 -6 & 0 ], B= [ cc -1 & -2 4 & 2 1 & 5 ] … - 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 $3 A-4 B+5 X=C$.

✓

Answer

$
\begin{aligned}
& 3 A-4 B+5 X=C \\
& \therefore 5 X=C-3 A+4 B \\
& =\left[\begin{array}{rr}
2 & 4 \\
-1 & -4 \\
-3 & 6
\end{array}\right]-3\left[\begin{array}{rr}
1 & -2 \\
3 & -5 \\
-6 & 0
\end{array}\right]+4\left[\begin{array}{rr}
-1 & -2 \\
4 & 2 \\
1 & 5
\end{array}\right] \\
& =\left[\begin{array}{rr}
2 & 4 \\
-1 & -4 \\
-3 & 6
\end{array}\right]-\left[\begin{array}{rr}
3 & -6 \\
9 & -15 \\
-18 & 0
\end{array}\right]+\left[\begin{array}{rr}
-4 & -8 \\
16 & 8 \\
4 & 20
\end{array}\right] \\
& =\left[\begin{array}{rr}
2-3+(-4) & 4-(-6)-8 \\
-1-9+16 & -4-(-15)+8 \\
-3-(-18)+4 & 6-0+20
\end{array}\right] \\
& =\left[\begin{array}{rr}
-5 & 2 \\
6 & 19 \\
19 & 26
\end{array}\right] \\
& \therefore X=\frac{1}{5}\left[\begin{array}{rr}
-5 & 2 \\
6 & 19 \\
19 & 26
\end{array}\right]=\left[\begin{array}{rr}
-1 & \frac{2}{5} \\
6 & \frac{19}{5} \\
5 & \frac{26}{5} \\
\frac{19}{5} & 5
\end{array}\right]
\end{aligned}
$

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