If x [ l 1 2 ]+y [ l 2 5 ]= [ l 4 9 ], then - Vidyadip

MCQ

If $x\left[\begin{array}{l}1 \\ 2\end{array}\right]+y\left[\begin{array}{l}2 \\ 5\end{array}\right]=\left[\begin{array}{l}4 \\ 9\end{array}\right],$ then

A
$x=1, y=2$
✓
$x=2, y=1$
C
$x=1, y=-1$
D
$x=3, y=2$

✓

Answer

Correct option: B.

$x=2, y=1$

We have, $x\left[\begin{array}{l}1 \\ 2\end{array}\right]+y\left[\begin{array}{l}2 \\ 5\end{array}\right]=\left[\begin{array}{l}4 \\ 9\end{array}\right]$
$\Rightarrow\left[\begin{array}{c} x+2 y \\ 2 x+5 y \end{array}\right]$
$=\left[\begin{array}{l} 4 \\ 9 \end{array}\right]$
$\Rightarrow x+2 y=4 ...(i)$
and $2 x+5 y=9 ........(ii)$
Solving $(i)$ and $(ii),$ we get $x=2, y=1$

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