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Find the value of $\lambda$ for which the set of equations $x+y-2z=0$, $2x-3y+z=0$, $x-5y+4z=\lambda$ are consistent.

(A) $\;\lambda=1$ (B) $\;\lambda=0$ (C) $\;\lambda=3$ (D) $\;\lambda=2$

1 Answer

A non-homogenous system has unique solution if $D\neq 0$ and infinite solutions if $D=D_1=D_2=D_3=0$
Now $D=\begin{vmatrix}1 &1 &-2\\2 &-3&1\\1 &-5&4\end{vmatrix}$$=0$
Hence $D_1,D_2,D_3$ should all be zero.i.e $D_1=0$
$\Rightarrow D_1=\begin{vmatrix}0 &1&-2\\0 &-3&1\\\lambda &5&4\end{vmatrix}=0$
$\Rightarrow \lambda(1-6)=0$
Hence (b) is the correct answer.
answered Nov 19, 2013 by sreemathi.v

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