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CBSE Class 12 Math 2025 All Sets Solved Paper

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Question : 6 of 20
Marks: +1, -0
If [x+y3y3xx+3]=[94x+yx+6y]\begin{bmatrix} x+y & 3 y \\ 3 x & x+3 \end{bmatrix} = \begin{bmatrix} 9 & 4 x+y \\ x+6 & y \end{bmatrix} then (x - y) = ?
Solution:  
[x+y3y3xx+3]=[94x+yx+6y]\begin{bmatrix} x+y & 3 y \\ 3 x & x+3 \end{bmatrix} = \begin{bmatrix} 9 & 4 x+y \\ x+6 & y \end{bmatrix}
If metrices are equal, then their corresponding entries must be equal
Sox+y=9…(i)\text{So} x+y=9 \ldots (i)
3y=4x+y…(ii)3y = 4x + y \ldots (ii)
3x=x+6…(iii)3x = x+6 \ldots (iii)
x+3=y…(iv)x+3 = y \ldots (iv)
From (iii) 2x=6⇒x+32x = 6 \Rightarrow x+3
Put x = 3 in (iv)
⇒3+3=y\Rightarrow 3+3=y
⇒y=6\Rightarrow y=6
Now (x - y) = (3 - 6) = -3
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