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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices3 Marks
Question
Evaluate: $\left[\begin{array}{rr}4 \sin 30^{\circ} & 2 \cos 60^{\circ} \\ \sin 90^{\circ} & 2 \cos 0^{\circ}\end{array}\right]\left[\begin{array}{ll}4 & 5 \\ 5 & 4\end{array}\right]$
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Answer

$\begin{aligned} & {\left[\begin{array}{cc}4 \sin 30^{\circ} & 2 \cos 60^{\circ} \\ \sin 90^{\circ} & 2 \cos 0^{\circ}\end{array}\right]\left[\begin{array}{ll}4 & 5 \\ 5 & 4\end{array}\right]} \\ & \sin 30^{\circ}=\frac{1}{2}, \cos 60^{\circ}=\frac{1}{2} \\ & \sin 90^{\circ}=1 \text { and } \cos 0^{\circ}=1 \\ & \therefore\left[\begin{array}{cc}4 \times \frac{1}{2} & 2 \times \frac{1}{2} \\ 1 & 2 \times 1\end{array}\right]\left[\begin{array}{ll}4 & 5 \\ 5 & 4\end{array}\right] \\ & =\left[\begin{array}{ll}2 & 1 \\ 1 & 2\end{array}\right]\left[\begin{array}{cc}4 & 5 \\ 5 & 4\end{array}\right] \\ & =\left[\begin{array}{ll}2 \times 4+1 \times 5 & 2 \times 5+1 \times 4 \\ 1 \times 4+2 \times 5 & 1 \times 5+2 \times 4\end{array}\right] \\ & =\left[\begin{array}{cc}8+5 & 10+4 \\ 4+10 & 5+8\end{array}\right] \\ & =\left[\begin{array}{ll}13 & 14 \\ 14 & 13\end{array}\right] .\end{aligned}$

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