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Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices3 Marks
Question
If $\text{x}\begin{bmatrix}2\\3 \end{bmatrix}+\text{y}\begin{bmatrix}-1\\1 \end{bmatrix}=\begin{bmatrix}10\\5 \end{bmatrix},$ find the value of x.
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Answer

$\text{x}\begin{bmatrix}2\\3 \end{bmatrix}+\text{y}\begin{bmatrix}-1\\1 \end{bmatrix}=\begin{bmatrix}10\\5 \end{bmatrix}$
$\Rightarrow\begin{bmatrix}2\text{x}-\text{y}\\3\text{x + y} \end{bmatrix}=\begin{bmatrix}10\\5 \end{bmatrix}$
Corresponding elements of equal matrices are equal.
⇒ 2x - y = 10 and 3x + y = 5
⇒ y = 2x - 10 and 3x + (2x - 10) = 5
⇒ y = 2x - 10 and 5x = 15
⇒ y = 2x - 10 and x = 3
⇒ y = 2(3) - 10 and x = 3
⇒ y = -4 and x = 3
$\therefore$ x = 3 and y = -4
Hence, the value of x is 3.

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