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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices3 Marks
Question
If $A=\left[\begin{array}{ll}3 & x \\ 0 & 1\end{array}\right]$ and $B=\left[\begin{array}{cc}9 & 16 \\ 0 & -y\end{array}\right]$ find $x$ and $y$ when $A^2 = B$
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Answer

Given $A=\left[\begin{array}{ll}3 & x \\ 0 & 1\end{array}\right] B=\left[\begin{array}{cc}9 & 16 \\ 0 & -y\end{array}\right]$ and $A^2=B$
Now, $A^2= A \times A$
$\begin{array}{l}=\left[\begin{array}{ll}3 & x \\ 0 & 1\end{array}\right] \times\left[\begin{array}{ll}3 & x \\ 0 & 1\end{array}\right] \end{array} $
$ =\left[\begin{array}{cc}9 & 3 x+x \\ 0 & 1\end{array}\right]  $
$ =\left[\begin{array}{cc}9 & 4 x \\ 0 & 1\end{array}\right]$
We have $A^2 = B$
Two matrices are equal if each and every corresponding element is equal.
$\Rightarrow\left[\begin{array}{cc}9 & 4 x \\ 0 & 1\end{array}\right]=\left[\begin{array}{cc}9 & 16 \\ 0 & -y\end{array}\right]$
$\Rightarrow 4 x=16$ and $1=-y$
$\Rightarrow x=4$ and $y=-1$

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