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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 $A=\left[\begin{array}{ll}2 & 5 \\ 3 & 7\end{array}\right], B=\left[\begin{array}{cc}1 & 7 \\ -3 & 0\end{array}\right]$, find the matrix $A-4 B+7 I$, where I is the unit matrix of order 2 .
✓

Answer

$
\begin{aligned}
A-4 B +7 I & =\left(\begin{array}{ll}
2 & 5 \\
3 & 7
\end{array}\right]-4\left[\begin{array}{rr}
1 & 7 \\
-3 & 0
\end{array}\right]+7\left[\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right] \\
& =\left[\begin{array}{rr}
2 & 5 \\
3 & 7
\end{array}\right]-\left[\begin{array}{rr}
4 & 28 \\
-12 & 0
\end{array}\right]+\left[\begin{array}{ll}
7 & 0 \\
0 & 7
\end{array}\right] \\
& =\left[\begin{array}{rr}
2-4+7 & 5-28+0 \\
3-(-12)+0 & 7-0+7
\end{array}\right] \\
& =\left[\begin{array}{rr}
5 & -23 \\
15 & 14
\end{array}\right] .
\end{aligned}
$

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