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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices3 Marks
Question
If $A=\left[\begin{array}{cc}2 & -1 \\ -4 & 5\end{array}\right]$ and $B=\left[\begin{array}{ll}0 & -3\end{array}\right]$ find the matrix $C$ such that $C A=B$
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Answer

$
A=\left[\begin{array}{cc}
2 & -1 \\
-4 & 5
\end{array}\right] \text { and } B=\left[\begin{array}{cc}
0 & -3
\end{array}\right]
$
Let matrix $C=\left[\begin{array}{ll}x & y\end{array}\right]$
Since the matrix $A$ is $2 \times 2$ and $B=7 \times 2$
$
\begin{aligned}
& \because C A=B \\
& \therefore(x y)\left[\begin{array}{cc}
2 & -1 \\
-4 & 5
\end{array}\right]=[0-3] \\
& =(2 x-4 y-x+5 y) \\
& =[0-3]
\end{aligned}
$
Comparing,
$
\begin{aligned}
& 2 x-4 y=0 \\
& \Rightarrow x-2 y=0 \\
& \therefore x=2 y
\end{aligned}
$
and
$
\begin{aligned}
& -x+5 y=-3 \\
& \Rightarrow-2 y+5 y=-3 \\
& \Rightarrow 3 y=-3 \\
& \Rightarrow y=-1 \\
& \therefore x=2 y \\
& =2 x(-1) \\
& =-2
\end{aligned}
$
Hence C
$
\begin{aligned}
& =\left[\begin{array}{ll}
x & y
\end{array}\right] \\
& =\left[\begin{array}{ll}
-2 & -1
\end{array}\right] .
\end{aligned}
$

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