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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices4 Marks
Question
If $A=\left[\begin{array}{ll}0 & -1 \\ 4 & -3\end{array}\right], B =\left[\begin{array}{c}-5 \\ 6\end{array}\right]$ and $3 A \times M =2 B$; Find matrix $M$
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Answer

Let the order of matrix $M$ be $a$ x $b.$
$3A \ x m = 2B$
$3\left[\begin{array}{ll}0 & -1 \\ 4 & -3\end{array}\right]_{2 \times 2} \times M_{a \times b}=2\left[\begin{array}{c}-5 \\ 6\end{array}\right]_{2 \times 1}$
Clearly the order of matrix $M$ is $2 x 1$
Let $M=\left[\begin{array}{l}x \\ y\end{array}\right]$
Then
$3\left[\begin{array}{ll}0 & -1 \\ 4 & -3\end{array}\right] \times\left[\begin{array}{l}x \\ y\end{array}\right]=2\left[\begin{array}{c}-5 \\ 6\end{array}\right] $
$ {\left[\begin{array}{cc}0 & -3 \\ 12 & -9\end{array}\right] \times\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{c}-10 \\ 2\end{array}\right]} $
$ {\left[\begin{array}{c}-3 y \\ 12 x-9 y\end{array}\right]=\left[\begin{array}{c}-10 12\end{array}\right]}$
Comparing the corressponding elements we get
$-3y = - 10$
$\Rightarrow y=\frac{10}{3}$
$12 x-9 y=12$
$=12 x=42$
$\Rightarrow x=\frac{7}{2} $
$ \therefore M=\left[\begin{array}{c}\frac{7}{2} \\ \frac{10}{3}\end{array}\right]$
 

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