If [ ll 1 & 2 2 & 9 ] [ l x y ]- [ l 20 90 ], then the values of … - Vidyadip

MCQ

If $\left[\begin{array}{ll}1 & 2 \\ 2 & 9\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]-\left[\begin{array}{l}20 \\ 90\end{array}\right]$, then the values of $x$ and $y$ are:

A
$x=10, y=0$
B
$x=5, y=4$
✓
$x=0, y=10$
D
$x=4, y=5$

✓

Answer

Correct option: C.

$x=0, y=10$

(c) $x=0, y=10$
Explanation:
$\begin{array}{l}{\left[\begin{array}{ll}1 & 2 \\ 2 & 9\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{l}20 \\ 90\end{array}\right]} \\ \Rightarrow\left[\begin{array}{l}1 \times x+2 \times y \\ 2 \times x+9 \times y\end{array}\right]=\left[\begin{array}{l}20 \\ 90\end{array}\right] \\ \Rightarrow\left[\begin{array}{r}x+2 y \\ 2 x+9 y\end{array}\right]=\left[\begin{array}{l}20 \\ 90\end{array}\right] \\ \Rightarrow x+2 y=20 \text { and } 2 x+9 y=90\end{array}$
Solving the two linear equations for $x$ and $y$, we get
x=0, y=10

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