Matrices & Determinants
Homogeneous System
MMTS_Full_Test_22
Grade 12
Question:
The system $(1-\lambda)x+3y-4z=0$, $x-(3+\lambda)y+5z=0$, $3x+y-\lambda z=0$ possesses non-trivial solutions for
exactly three distinct real values of $\lambda$
exactly two distinct real values of $\lambda$
exactly one real value of $\lambda$
infinite number of distinct real values of $\lambda$
Step-by-Step Solution
Key Concept: Set determinant of coefficient matrix = 0
$\Delta=0$ gives: $\lambda(\lambda^2-\lambda-6)=0\Rightarrow\lambda=0,3,-2$. Three distinct real values.
Correct Answer: 2