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Matrices (p-1) — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Matrices (p-1)2 Marks
Question
If $A=\left[\begin{array}{cc}5 & 4 \\ -2 & 3\end{array}\right]$ and $B=\left[\begin{array}{cc}-1 & 3 \\ 4 & -1\end{array}\right]$, then find $C^{\top}$, such that $3 A-$ $2 B + C = I$, where $I$ is the unit matrix of order 2 .
✓

Answer

$
\begin{aligned}
& 3 A -2 B + C = I \\
& \therefore C = I -3 A +2 B \\
& =\left(\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right)-3\left(\begin{array}{rr}
5 & 4 \\
-2 & 3
\end{array}\right)+2\left(\begin{array}{rr}
-1 & 3 \\
4 & -1
\end{array}\right) \\
& =\left[\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right]-\left[\begin{array}{rr}
15 & 12 \\
-6 & 9
\end{array}\right]+\left[\begin{array}{rr}
-2 & 6 \\
8 & -2
\end{array}\right] \\
& =\left(\begin{array}{rr}
1-15+(-2) & 0-12+6 \\
0-(-6)+8 & 1-9-2
\end{array}\right) \\
& \therefore C=\left[\begin{array}{rr}
-16 & -6 \\
14 & -10
\end{array}\right] \\
& \therefore C^T=\left(\begin{array}{rr}
-16 & 14 \\
-6 & -10
\end{array}\right) \text {. } \\
&
\end{aligned}
$

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