Question

The value of $\lambda$ for which the system of equations
$(1-\lambda) x+3 y-4 z=0 $
$x-(3+\lambda) y+5 z=0$
$3 x+y-\lambda z=0$
possesses non-trivial solutions is(are)

• A. -1
• B. 0
• C. 1
• D. 2

Answer 1

Answer: (A), (B)

Put $\quad\begin{vmatrix}(1-\lambda) & 3 & -4 \\ 1 & -(3+\lambda) & 5 \\ 3 & 1 & -\lambda\end{vmatrix}=0$
$\Rightarrow \lambda(\lambda+1)^2=0 \Rightarrow \lambda=-1,0$