3 and 4 .Determinants and Matrices
medium

If $x + y - z = 0,\,3x - \alpha y - 3z = 0,\,\,x - 3y + z = 0$ has non zero solution, then $\alpha = $

A

$-1$

B

$0$

C

$1$

D

$-3$

Solution

(d) The given system of homogeneous equations has a non-zero solution if,

$\Delta = 0$ i.e., $\left| {\,\begin{array}{*{20}{c}}1&{\,\,\,1}&{ – 1}\\3&{ – \alpha }&{ – 3}\\1&{ – 3}&{\,\,\,1}\end{array}\,} \right| = – 2\alpha – 6 = 0$,i.e. if $\alpha = – 3$.

Standard 12
Mathematics

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