MCQ
If $\left[\begin{array}{ll}2 & 0 \\ 0 & 4\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{c}2 \\ -8\end{array}\right]$, the value of $x$ and $y$ respectively are:
- ✓$1,-2$
- B$-2,1$
- C1,2
- D$-2,-1$
✓
Answer
Correct option: A.
$1,-2$
(a) $1,-2$
Explanation:
$\begin{array}{l}{\left[\begin{array}{ll}2 & 0 \\ 0 & 4\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{r}2 \\ -8\end{array}\right]} \\ {\left[\begin{array}{l}2 x+0 y \\ 0 x+4 y\end{array}\right]=\left[\begin{array}{r}2 \\ -8\end{array}\right]} \\ {\left[\begin{array}{l}2 x \\ 4 y\end{array}\right]=\left[\begin{array}{r}2 \\ -8\end{array}\right]}\end{array}$
On equating the corresponding terms,
$2 x=2 \Rightarrow x=1$
and $4 y=-8 \Rightarrow y=-2$
$(1,-2) \text { Ans. }$
Explanation:
$\begin{array}{l}{\left[\begin{array}{ll}2 & 0 \\ 0 & 4\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{r}2 \\ -8\end{array}\right]} \\ {\left[\begin{array}{l}2 x+0 y \\ 0 x+4 y\end{array}\right]=\left[\begin{array}{r}2 \\ -8\end{array}\right]} \\ {\left[\begin{array}{l}2 x \\ 4 y\end{array}\right]=\left[\begin{array}{r}2 \\ -8\end{array}\right]}\end{array}$
On equating the corresponding terms,
$2 x=2 \Rightarrow x=1$
and $4 y=-8 \Rightarrow y=-2$
$(1,-2) \text { Ans. }$
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