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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices3 Marks
Question
Given $A=\left[\begin{array}{cc}3 & -2 \\ -1 & 4\end{array}\right] B=\left[\begin{array}{l}6 \\ 1\end{array}\right], C=\left[\begin{array}{c}-4 \\ 5\end{array}\right]$ and $D=\left[\begin{array}{l}2 \\ 2\end{array}\right]$ Find $AB + 2 C-4 D$
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Answer

$\begin{array}{l} AB =\left[\begin{array}{cc}3 & -2 \\ -1 & 4\end{array}\right]\left[\begin{array}{l}6 \\ 1\end{array}\right]=\left[\begin{array}{c}18-2 \\ -6+4\end{array}\right]\end{array} =\left[\begin{array}{c}16 \\ -2\end{array}\right]  $
$ 2 C =2\left[\begin{array}{c}-4 \\ 5\end{array}\right]=\left[\begin{array}{c}-8 \\ 10\end{array}\right]  $
$ 4 D =4\left[\begin{array}{l}2 \\ 2\end{array}\right]$
$=\left[\begin{array}{l}8 \\ 8\end{array}\right]  $
$ \text { Now, } AB +2 C -4 D $
$=\left[\begin{array}{c}16 \\ -2\end{array}\right]+\left[\begin{array}{c}-8 \\ 10\end{array}\right]-\left[\begin{array}{l}8 \\ 8\end{array}\right] \\ $
$=\left[\begin{array}{c}16-8-8 \\ -2+10-8\end{array}\right] \\ $
$=\left[\begin{array}{l}0 \\ 0\end{array}\right]$

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