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3 and 4 .Determinants and Matrices
medium
$x + ky - z = 0,3x - ky - z = 0$ and $x - 3y + z = 0$ has non-zero solution for $k =$
A
$-1$
B
$0$
C
$1$
D
$2$
(IIT-1988)
Solution
(c) It has a non-zero solution if
$\left| {\,\begin{array}{*{20}{c}}1&{\,\,k}&{ – 1}\\3&{ – k}&{ – 1}\\1&{ – 3}&{\,\,1}\end{array}} \right| =0$
$ \Rightarrow – 6k + 6 = 0 \Rightarrow k = 1$.
Standard 12
Mathematics