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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices2 Marks
Question
Solve the matrix equation $: \left[\begin{array}{l}4 \\ 1\end{array}\right], X =\left[\begin{array}{ll}-4 & 8 \\ -1 & 2\end{array}\right]$
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Answer

$\left[\begin{array}{l}4 \\ 1\end{array}\right], X=\left[\begin{array}{ll}-4 & 8 \\ -1 & 2\end{array}\right]$
Let matrix $X=[x y]$
$\therefore\left[\frac{4}{1}\right][x, y]=\left[\begin{array}{ll}-4 & 8 \\ -1 & 2\end{array}\right]$
$\Rightarrow\left[\begin{array}{cc}4 x & 4 y \\ x & y\end{array}\right]=\left[\begin{array}{ll}-4 & 8 \\ -1 & 2\end{array}\right]$
Comparing the corresponding elements
$4 x=-4 \Rightarrow x=-1$
$ 4 y=8 \Rightarrow y=2$
$ \therefore x=[-1 2] .$

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