If \( \begin{bmatrix}0 & x\\2 & 1\end{bmatrix}+2\begin{bmatrix}3 & 1\\y & 0\end{bmatrix}=\begin{bmatrix}6 & 5\\8 & 1\end{bmatrix} \), then the value of \( 2x+3y \) is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 15
Multiplying the second matrix by 2 and adding,
\( \displaystyle \begin{bmatrix}0 & x\\2 & 1\end{bmatrix}+\begin{bmatrix}6 & 2\\2y & 0\end{bmatrix}=\begin{bmatrix}6 & x+2\\2+2y & 1\end{bmatrix} \)
Equal matrices have equal corresponding entries:
\( \displaystyle x+2=5\ \Rightarrow\ x=3 \)
\( \displaystyle 2+2y=8\ \Rightarrow\ y=3 \)
\( \displaystyle 2x+3y=6+9=15 \)