If \( \begin{bmatrix}x-2y & z\\ 3x+y & w\end{bmatrix}=\begin{bmatrix}1 & 2\\ -11 & 1\end{bmatrix} \); then the value of \( y-x \) is:-
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1
Two matrices are equal when their corresponding entries are equal. Comparing the first column:
\( \displaystyle x-2y=1 \)
\( \displaystyle 3x+y=-11 \)
From the first equation \( x=1+2y \). Putting this in the second:
\( \displaystyle 3(1+2y)+y=-11 \)
\( \displaystyle 7y=-14 \)
\( \displaystyle y=-2 \)
Then \( x=1+2(-2)=-3 \), so
\( \displaystyle y-x=-2-(-3) \)
\( \displaystyle =1 \)