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Algebra of Matrices — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSAlgebra of Matrices2 Marks
Question
If $2\begin{bmatrix}3&4\\5&\text{x} \end{bmatrix}+\begin{bmatrix}1&\text{y}\\0&1 \end{bmatrix}=\begin{bmatrix}7&0\\10&5 \end{bmatrix},$ find x - y.
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Answer

$2\begin{bmatrix}3&4\\5&\text{x} \end{bmatrix}+\begin{bmatrix}1&\text{y}\\0&1 \end{bmatrix}=\begin{bmatrix}7&0\\10&5 \end{bmatrix}$
$\Rightarrow\begin{bmatrix}6+1&8+\text{y}\\10+0&2\text{x}+1 \end{bmatrix}=\begin{bmatrix}7&0\\10&5 \end{bmatrix}$
$\Rightarrow\begin{bmatrix}7&8+\text{y}\\10&2\text{x}+1 \end{bmatrix}=\begin{bmatrix}7&0\\10&5 \end{bmatrix}$
⇒ 8 + y = 0 and 2x + 1 = 5
⇒ y = - 8 and 2x = 4
⇒ y = - 8 and x = 2
Hence, x - y = 2 - (- 8) = 10.

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