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निम्नलिखित समीकरण से $x$ तथा $y$ के मानों को ज्ञात कीजिए:
$2\left[\begin{array}{cc}x & 5 \\ 7 & y-3\end{array}\right]+\left[\begin{array}{rr}3 & -4 \\ 1 & 2\end{array}\right]=\left[\begin{array}{rr}7 & 6 \\ 15 & 14\end{array}\right]$
$x=2$, $y=9$
$x=2$, $y=9$
$x=2$, $y=9$
$x=2$, $y=9$
Solution
$2\left[ {\begin{array}{*{20}{c}}
x&5 \\
7&{y – 3}
\end{array}} \right] + \left[ {\begin{array}{*{20}{c}}
3&{ – 4} \\
1&2
\end{array}} \right]$ $ = \left[ {\begin{array}{*{20}{c}}
7&6 \\
{15}&{14}
\end{array}} \right] \Rightarrow $ $\left[ {\begin{array}{*{20}{c}}
{2x}&{10} \\
{14}&{2y – 6}
\end{array}} \right] + $ $\left[ {\begin{array}{*{20}{c}}
3&{ – 4} \\
1&2
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
7&6 \\
{15}&{14}
\end{array}} \right]$
or $\left[ {\begin{array}{*{20}{c}}
{2x + 3}&{10 – 4} \\
{14 + 1}&{2y – 6 + 2}
\end{array}} \right]$ $ = \left[ {\begin{array}{*{20}{c}}
7&6 \\
{15}&{14}
\end{array}} \right] \Rightarrow $ $\left[ {\begin{array}{*{20}{c}}
{2x + 3}&6 \\
{15}&{2y – 4}
\end{array}} \right]$ $ = \left[ {\begin{array}{*{20}{c}}
7&6 \\
{15}&{14}
\end{array}} \right]$
or $2 x+3=7$ and $2 y-4=14$ (Why ?)
or $2 x=7-3$ and $2 y=18$
or $x=\frac{4}{2}$ and $y=\frac{18}{2}$
i.e. $x=2$ and $y=9$.
