If \( \begin{bmatrix} -2 & 0\\ x & 4\end{bmatrix}+3\begin{bmatrix} y & 0\\ 2 & -1\end{bmatrix}=I \), where \( I \) is \( 2\times 2 \) unit matrix, then the value of \( x \) and \( y \) are:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( x=-6,y=1 \)
Multiplying the second matrix by 3 and adding entry by entry:
\( \displaystyle \begin{bmatrix} -2 & 0\\ x & 4\end{bmatrix}+\begin{bmatrix} 3y & 0\\ 6 & -3\end{bmatrix}=\begin{bmatrix} 3y-2 & 0\\ x+6 & 1\end{bmatrix} \)
This equals \( I=\begin{bmatrix} 1 & 0\\ 0 & 1\end{bmatrix} \), so comparing the entries:
\( \displaystyle 3y-2=1\ \Rightarrow\ y=1 \)
\( \displaystyle x+6=0\ \Rightarrow\ x=-6 \)