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Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices4 Marks
Question
$\begin{bmatrix}2&3\\5&7\end{bmatrix}\begin{bmatrix}1&-3\\-2&4\end{bmatrix}=\begin{bmatrix}-4&6\\-9&\text{x}\end{bmatrix}$ find x.
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Answer

Given: $\begin{bmatrix}2&3\\5&7\end{bmatrix}\begin{bmatrix}1&-3\\-2&4\end{bmatrix}=\begin{bmatrix}-4&6\\-9&\text{x}\end{bmatrix}$
$\Rightarrow\begin{bmatrix}2-6&-6+12\\5-14&-15+28\end{bmatrix}=\begin{bmatrix}-4&6\\-9&\text{x} \end{bmatrix}$
$\Rightarrow\begin{bmatrix}-4&6\\-9&\text{x} \end{bmatrix}=\begin{bmatrix}-4&6\\-9&\text{x} \end{bmatrix}$
$\Rightarrow\text{x}=3$
$\therefore\ \text{x}=13$

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