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Algebra of Matrices — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSAlgebra of Matrices2 Marks
Question
Find x, y satisfying the matrix equation.
$\text{x}\begin{bmatrix}2\\1\end{bmatrix}+\text{y}\begin{bmatrix}3\\5\end{bmatrix}+\begin{bmatrix}-8\\-11\end{bmatrix}=0$
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Answer

Given: $\text{x}\begin{bmatrix}2\\1\end{bmatrix}+\text{y}\begin{bmatrix}3\\5\end{bmatrix}+\begin{bmatrix}-8\\-11\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix}$
$\Rightarrow\begin{bmatrix}2\text{x}+3\text{y}-8\\\text{x}+5\text{y}-11\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix}$
$\Rightarrow2\text{x}+3\text{y}-8=0$
$\Rightarrow2\text{x}+3\text{y}=8\ \dots(1)$
Also,
$\text{x}+5\text{y}-11=0$
$\Rightarrow\text{x}+5\text{y}=11$
$\Rightarrow\text{x}=11-5\text{y}\ \dots(2)$
Putting the value of x in eq. (1), we get
$2(11-5\text{y})+3\text{y}=8$
$\Rightarrow22-10\text{y}+3\text{y}=8$
$\Rightarrow-7\text{y}=8-22$
$\Rightarrow-7\text{y}=-14$
$\Rightarrow\text{y}=2$
Putting the value of y in eq. (2), we get
$\text{x}=11-5(2)$
$\Rightarrow\text{x}=11-10$
$\Rightarrow\text{x}=1$
$\therefore\ \text{x}=1$ and $\text{y}=2$

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