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3 and 4 .Determinants and Matrices
hard
સમીકરણની સંહતિ $\begin{array}{l}\alpha x + y + z = \alpha - 1\\x + \alpha y + z = \alpha - 1\\x + y + \alpha z = \alpha - 1\end{array}$ નો ઉકેલ ખાલીગણ હોય તો $\alpha $ કિમત મેળવો.
A
$-2 $ નથી
B
$1$
C
$-2$
D
$-2 $ અથવા $1 $
(AIEEE-2005)
Solution
(c) For no solution or infinitely many solutions $\left| {\,\begin{array}{*{20}{c}}\alpha &1&1\\1&\alpha &1\\1&1&\alpha \end{array}\,} \right| = 0 \Rightarrow \alpha = 1,\alpha = – 2$.
But for $\alpha = 1$, clearly there are infinitely many solutions and when we put $\alpha = – 2$ in given system of equations and adding them together
$L.H.S$ $ \ne $ $R.H.S$.
i.e., No solution.
Standard 12
Mathematics
