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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 $A=\left[\begin{array}{cc}1 & -2 \\ 5 & 3\end{array}\right], B=\left[\begin{array}{cc}1 & -3 \\ 4 & -7\end{array}\right]$, then find the matrix $A-2 B+6 I$, where $I$ is the unit matrix of order 2 .
✓

Answer

$
\begin{aligned}
A-2 B+6 I & =\left[\begin{array}{rr}
1 & -2 \\
5 & 3
\end{array}\right]-2\left[\begin{array}{ll}
1 & -3 \\
4 & -7
\end{array}\right]+6\left[\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right] \\
& =\left[\begin{array}{rr}
1 & -2 \\
5 & 3
\end{array}\right]-\left[\begin{array}{rr}
2 & -6 \\
8 & -14
\end{array}\right]+\left[\begin{array}{ll}
6 & 0 \\
0 & 6
\end{array}\right] \\
& =\left[\begin{array}{rr}
1-2+6 & -2-(-6)+0 \\
5-8+0 & 3-(-14)+6
\end{array}\right] \\
& =\left[\begin{array}{rr}
5 & 4 \\
-3 & 23
\end{array}\right]
\end{aligned}
$

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