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3 and 4 .Determinants and Matrices
normal
$m$ ની કેટલી કિમંતો માટે રેખાઓ $x + y - 1 = 0$, $(m - 1) x + (m^2 - 7) y - 5 = 0 \,\,\&\,\, (m - 2) x + (2m - 5) y = 0$ ઓ સંગામી થાય.
A
$0$
B
$1$
C
$2$
D
$3$
Solution
$\left| {\begin{array}{*{20}{c}}
1&1&{ – 1}\\
{m – 1}&{{m^2} – 7}&{ – 5}\\
{m – 2}&{2m – 5}&0
\end{array} = 0} \right.$
$m^{3}-4 m^{2}+5 m-6=0$
$\left(m^{2}-m+2\right)(m-3)=0$
$\mathrm{D}<0$ of $\mathrm{m}^{2}-\mathrm{m}+2=0$
so, $m=3,$ but at $\mathrm{m}=3$ lines are parellel, so no. of values of $\mathrm{m}$ is zero.
Standard 12
Mathematics
