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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices2 Marks
Question
If $A=\left[\begin{array}{ll}1 & 2 \\ 2 & 3\end{array}\right]$ and $B=\left[\begin{array}{ll}2 & 1 \\ 3 & 2\end{array}\right], C=\left[\begin{array}{ll}1 & 3 \\ 3 & 1\end{array}\right]$ find the matrix $C(B-A)$
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Answer

$\begin{aligned} & A=\left[\begin{array}{ll}1 & 2 \\ 2 & 3\end{array}\right] \\ & B=\left[\begin{array}{ll}2 & 1 \\ 3 & 2\end{array}\right] \\ & C=\left[\begin{array}{ll}1 & 3 \\ 3 & 1\end{array}\right] \\ & B-A=\left[\begin{array}{ll}2 & 1 \\ 3 & 2\end{array}\right]-\left[\begin{array}{ll}1 & 2 \\ 2 & 3\end{array}\right] \\ & =\left[\begin{array}{ll}1 & -1 \\ 1 & -1\end{array}\right] \\ & C(B-A)=\left[\begin{array}{ll}1 & 3 \\ 3 & 1\end{array}\right] \times\left[\begin{array}{ll}1 & -1 \\ 1 & -1\end{array}\right] \\ & =\left[\begin{array}{ll}1+3 & -1-3 \\ 3+1 & -3-1\end{array}\right] \\ & =\left[\begin{array}{ll}4 & -4 \\ 4 & -4\end{array}\right] . \\ & \end{aligned}$

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