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જો ત્રણ વાસ્તવિક સંખ્યાઓ $p, q, r$ એ શ્રેણિક સમીકરણ $[p\,q\,r]\,\left[ {\begin{array}{*{20}{c}}
3&4&1\\
3&2&3\\
2&0&2
\end{array}} \right] = [3\,\,\,0\,\,\,1]$ નું પાલન કરે છે તો $2p + q - r$ મેળવો.
$-3$
$-1$
$4$
$2$
Solution
Given
$\left[ {\begin{array}{*{20}{c}}
p&q&r
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
3&4&1\\
3&2&3\\
2&0&2
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
3&0&1
\end{array}} \right]$
$ \Rightarrow \left[ {\begin{array}{*{20}{c}}
{3p + 3q + 2r}&{4p + 2q}&{p + 3q + 2r}
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
3&0&1
\end{array}} \right]$
$ \Rightarrow 3p + 3q + 2r = 3\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,….\left( i \right)$
$4p + 2q = 0 \Rightarrow q = – 2p\,\,\,\,\,\,\,\,……\left( {ii} \right)$
$p + 3q + 2r = 1\,\,\,\,\,\,\,\,\,\,…….\left( {iii} \right)$
On solving $(i),(ii)$ and $(iii)$ , we get
$p=1,q=-2,r=3$
$\therefore 2p + q + r = 2\left( 1 \right) + \left( { – 2} \right) – \left( 3 \right) = – 3$.
