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If $$\displaystyle x\left[ \begin{matrix} 2 \\ 3 \end{matrix} \right] +y\left[ \begin{matrix} -1 \\ 1 \end{matrix} \right] =\left[ \begin{matrix} 10 \\ 5 \end{matrix} \right] $$
Find values of $$x$$ and $$y$$.


Solution

$$\displaystyle x\left[ \begin{matrix} 2 \\ 3 \end{matrix} \right]
+y\left[ \begin{matrix} -1 \\ 1 \end{matrix} \right] =\left[
\begin{matrix} 10 \\ 5 \end{matrix} \right] $$
$$\displaystyle
\Rightarrow \left[ \begin{matrix} 2x \\ 3x \end{matrix} \right] +\left[
\begin{matrix} -y \\ y \end{matrix} \right] =\left[ \begin{matrix} 10 \\
5 \end{matrix} \right] $$
$$\displaystyle \Rightarrow \left[
\begin{matrix} 2x-y \\ 3x+y \end{matrix} \right] =\left[ \begin{matrix}
10 \\ 5 \end{matrix} \right] $$
Comparing the corresponding elements of these two matrices,
we get  $$\displaystyle 2x-y=10$$ and $$\displaystyle 3x+y=5$$
Solving these we get,
$$\displaystyle x=3\quad$$ and  $$\quad y=-4$$

Mathematics
NCERT
Standard XII

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