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Matrices — Mathematics STD 10 — Question

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

$
\begin{aligned}
& A=\left[\begin{array}{cc}
2 & 12 \\
0 & 1
\end{array}\right] \text { and } \\
& B=\left[\begin{array}{ll}
4 & x \\
0 & 1
\end{array}\right] \\
& A^2=B \\
& \Rightarrow A \times A=B \\
& \Rightarrow\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}{ll}
4 & x \\
0 & 1
\end{array}\right] \\
& \Rightarrow\left[\begin{array}{cc}
2 \times 2+12 \times 0 & 2 \times 12+12 \times 1 \\
0 \times 2+1 \times 0 & 0 \times 12+1 \times 1
\end{array}\right]=\left[\begin{array}{ll}
4 & x \\
0 & 1
\end{array}\right] \\
& \Rightarrow\left[\begin{array}{cc}
4+0 & 24+12 \\
0+0 & 0+1
\end{array}\right]=\left[\begin{array}{cc}
4 & x \\
0 & 1
\end{array}\right] \\
& \Rightarrow\left[\begin{array}{cc}
4 & 36 \\
0 & 1
\end{array}\right]=\left[\begin{array}{ll}
4 & x \\
0 & 1
\end{array}\right]
\end{aligned}
$
Comparing the corresponding elements of two equal matrices, $x=36$.

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