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Algebra of Matrices — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
Question
If $\begin{bmatrix}\text{x}&\text{x}-\text{y}\\2\text{x+y}&7 \end{bmatrix}=\begin{bmatrix}3&1\\8&7 \end{bmatrix},$ then find the value of y.
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Answer

We have, $\begin{bmatrix}\text{x}&\text{x}-\text{y}\\2\text{x+y}&7 \end{bmatrix}=\begin{bmatrix}3&1\\8&7 \end{bmatrix}$
The corresponding elements of two equal matrices are equal.
$\therefore$ x = 3
x - y = 1 ...(1)
Putting the value of x in eq. (1)
3 - y = 1
⇒ 3 - 1 = y
$\therefore$ y = 2

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