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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices3 Marks
Question
Find the value of $x$, given that $A^2=B$
$A=\left[\begin{array}{cc}2 & 12 \\ 0 & 1\end{array}\right]$ and $B=\left[\begin{array}{ll}4 & x \\ 0 & 1\end{array}\right]$
✓

Answer

$A=\left[\begin{array}{cc}2 & 12 \\ 0 & 1\end{array}\right]$
$A^2=\left[\begin{array}{cc}2 & 12 \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}2 & 12 \\ 0 & 1\end{array}\right]=\left[\begin{array}{cc}4+0 & 24+12 \\ 0+0 & 0+1\end{array}\right]=\left[\begin{array}{cc}4 & 36 \\ 0 & 1\end{array}\right]$
Given $A^2=B$
$\therefore\left[\begin{array}{cc}4 & 36 \\ 0 & 1\end{array}\right]=\left[\begin{array}{ll}4 & x \\ 0 & 1\end{array}\right]$
Comparing the corresponding elements we get
x = 36

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