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

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