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MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES3 Marks
Question
If $\begin{bmatrix}2&1&3\end{bmatrix}\begin{bmatrix}-1&0&-1\\-1&1&0\\0&1&1\end{bmatrix}\begin{bmatrix}1\\0\\-1\end{bmatrix}=\text{A},$ then find the value of A.
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Answer

We have, $\begin{bmatrix}2&1&3\end{bmatrix}_{1\times3}\begin{bmatrix}-1&0&-1\\-1&1&0\\0&1&1\end{bmatrix}_{3\times3}\begin{bmatrix}1\\0\\-1\end{bmatrix}_{3\times1}=\text{A}$ $\therefore\ \begin{bmatrix}2&1&3\end{bmatrix}_{1\times3}\begin{bmatrix}-1+0+1\\-1+0+0\\0+0-1\end{bmatrix}_{3\times1}=\text{A}$$\Rightarrow\ \begin{bmatrix}2&1&3\end{bmatrix}_{1\times3}\begin{bmatrix}0\\-1\\-1\end{bmatrix}_{3\times1}=\text{A}$
$\Rightarrow\ [0-1-3]=\text{A}$
$\Rightarrow\ \text{A}=[-4]$

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