QQuestion
If \begin{bmatrix}2&0\\0&4\end{bmatrix}\begin{bmatrix}\mathrm{x}\\\mathrm{y}\end{bmatrix}=\begin{bmatrix}2\\-8\end{bmatrix}, the values of x and y respectively are:
(a) 1, −2
(b) −2, 1
(c) 1, 2
(d) −2, −1
✓Answer
(a) 1, −2
Explanation:
\begin{bmatrix}2&0\\0&4\end{bmatrix}\begin{bmatrix}\mathrm{x}\\\mathrm{y}\end{bmatrix}=\begin{bmatrix}2\\-8\end{bmatrix}⇒ \begin{bmatrix}2\mathrm{x}\\4\mathrm{y}\end{bmatrix}=\begin{bmatrix}2\\-8\end{bmatrix}
⇒ 2x = 2 and 4y = −8.
∴ x = 1 and y = −2.
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