MCQ
If $x \begin{bmatrix} 2 \\ 3\end{bmatrix} +y \begin{bmatrix} -1 \\ 0 \end{bmatrix} = \begin{bmatrix} 10 \\ 6\end{bmatrix} $ then the values of $x$ and $y$ are
- A$x=2, y=6$
- ✓$x=2, y=-6$
- C$x=3, y=-4$
- D$x=3, y=-6$
✓
Answer
Correct option: B.
$x=2, y=-6$
Given
$x \begin{bmatrix} 2 \\ 3\end{bmatrix} +y \begin{bmatrix} -1 \\ 0 \end{bmatrix} = \begin{bmatrix} 10 \\ 6\end{bmatrix} $
$ \begin{bmatrix} 2x \\ 3x\end{bmatrix} +y \begin{bmatrix} -y \\ 0 \end{bmatrix} = \begin{bmatrix} 10 \\ 6\end{bmatrix} $
$ \begin{bmatrix} 2x-y \\ 3x+0\end{bmatrix} = \begin{bmatrix} 10 \\ 6\end{bmatrix} $
Comapring, we get
$ 3 x =6 \Rightarrow x =\frac{6}{3}=2$ and
$ 2 x-y=10 $
$ 2 \times 2-y=10 $
$ \Rightarrow 4-y=10 $
$ \Rightarrow-y=10-4=6 $
$ \Rightarrow y=-6 $
$ \therefore x=2, y=-6 .$
$x \begin{bmatrix} 2 \\ 3\end{bmatrix} +y \begin{bmatrix} -1 \\ 0 \end{bmatrix} = \begin{bmatrix} 10 \\ 6\end{bmatrix} $
$ \begin{bmatrix} 2x \\ 3x\end{bmatrix} +y \begin{bmatrix} -y \\ 0 \end{bmatrix} = \begin{bmatrix} 10 \\ 6\end{bmatrix} $
$ \begin{bmatrix} 2x-y \\ 3x+0\end{bmatrix} = \begin{bmatrix} 10 \\ 6\end{bmatrix} $
Comapring, we get
$ 3 x =6 \Rightarrow x =\frac{6}{3}=2$ and
$ 2 x-y=10 $
$ 2 \times 2-y=10 $
$ \Rightarrow 4-y=10 $
$ \Rightarrow-y=10-4=6 $
$ \Rightarrow y=-6 $
$ \therefore x=2, y=-6 .$
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