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જો સમીકરણ સહંતિ $\left( {\begin{array}{*{20}{c}}
1&{ - 2}&5\\
2&{ - 1}&1\\
{11}&{ - 7}&p
\end{array}} \right)\left( {\begin{array}{*{20}{c}}
x\\
y\\
z
\end{array}} \right) = \left( {\begin{array}{*{20}{c}}
3\\
1\\
q
\end{array}} \right)$ ને અનંત ઉકેલ હોય તો . . . .
$p + q = 2$
$p + q = 10$
$p -q = 2$
એકપણ નહીં.
Solution
$x-2 y+5 z=3$
$2 x-y+z=1$
$11 x-7 y+p z=q$
$\Delta=0 \Rightarrow\left|\begin{array}{ccc}{1} & {-2} & {5} \\ {2} & {-1} & {1} \\ {11} & {-7} & {\mathrm{p}}\end{array}\right|=0$
$(-p+7)+2(2 p-11)+5(-14+11)=0$
$\Rightarrow \quad \mathrm{p}=10$
${\Delta _{\rm{x}}} = 0 \Rightarrow \left| {\begin{array}{*{20}{c}}
3&2&5\\
1&1&1\\
{\rm{q}}&7&{10}
\end{array}} \right| = 0$
$\Rightarrow \quad 3(10-7)-2(10-q)+5(7-q)=0$
$\Rightarrow \quad \mathrm{q}=8$
$p-q=2$
