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Determinants and Matrices — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsDeterminants and Matrices1 Mark
Question
Find $x, y$ if $\left\{-1\left[\begin{array}{lll}1 & 2 & 1 \\ 2 & 0 & 3\end{array}\right]+3\left[\begin{array}{lll}2 & -3 & 7 \\ 1 & -1 & 3\end{array}\right]\right\}\left[\begin{array}{c}5 \\ 0 \\ -1\end{array}\right]=\left[\begin{array}{l}x \\ y\end{array}\right]$
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Answer

$\left\{-1\left[\begin{array}{lll}1 & 2 & 1 \\ 2 & 0 & 3\end{array}\right]+3\left[\begin{array}{lll}2 & -3 & 7 \\ 1 & -1 & 3\end{array}\right]\right\}\left[\begin{array}{c}5 \\ 0 \\ -1\end{array}\right]=\left[\begin{array}{l}x \\ y\end{array}\right]$
$\therefore \left\{\left[\begin{array}{ccc}-1 & -2 & -1 \\ -2 & 0 & -3\end{array}\right]+\left[\begin{array}{ccc}6 & -9 & 21 \\ 3 & -3 & 9\end{array}\right]\right\}\left[\begin{array}{c}5 \\ 0 \\ -1\end{array}\right]=\left[\begin{array}{l}x \\ y\end{array}\right]$
$\therefore \left[\begin{array}{ccc}5 & -11 & 20 \\ 1 & -3 & 6\end{array}\right]\left[\begin{array}{c}5 \\ 0 \\ -1\end{array}\right]=\left[\begin{array}{l}x \\ y\end{array}\right]$
$\therefore \left[\begin{array}{c}25-0-20 \\ 5-0-6\end{array}\right]=\left[\begin{array}{l}x \\ y\end{array}\right]$
$\therefore \left[\begin{array}{c}5 \\ -1\end{array}\right]=\left[\begin{array}{l}x \\ y\end{array}\right]$
$\therefore $ By equality of matrices, we get
$x=5, y=-1$

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