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3 and 4 .Determinants and Matrices
medium
ધારો કે સુરેખ સમીકરણ સંહતિ $x +2 y + z =2$, $\alpha x +3 y - z =\alpha,-\alpha x + y +2 z =-\alpha$ સુસંગત નથી.તો $\alpha=\dots\dots\dots\dots$
A
$\frac{5}{2}$
B
$\frac{7}{2}$
C
$-\frac{7}{2}$
D
$-\frac{5}{2}$
(JEE MAIN-2022)
Solution
$\Delta=\left|\begin{array}{ccc} 1 & 2 & 1 \\ 2 & 3 & -1 \\ -2 & 1 & 2 \end{array}\right|$
$=(6+ y )-2((2 \alpha-\alpha)+1(\alpha+3 \alpha)$
$=7-2 \alpha+4 \alpha$
$=7+2 \alpha$
$\Delta=0 \Rightarrow \alpha=-\frac{7}{2}$
$\Delta_{1}=\left|\begin{array}{ccc}2 & 2 & 1 \\ \alpha & 3 & -1 \\ -\alpha & 1 &2\end{array}\right|$
$=14+2 \alpha$
$\alpha=-x_{2}=7$
$\Delta_{1} \neq 0$
Standard 12
Mathematics
