JEE Main 2020 (Online) 6th September Evening ShiftQuestion 1
The sum of distinct values of $\lambda$ for which the system of equations $(\lambda-1)x+(3\lambda+1)y+2\lambda z=0$, $(\lambda-1)x+(4\lambda-2)y+(\lambda+3)z=0$, $2x+(3\lambda+1)y+3(\lambda-1)z=0$, has non-zero solutions, is ________.
Determinant
Answer$3$
Solution
Non-zero solutions need the determinant $=0$. Expanding gives $6\lambda(\lambda-3)^2=0$. Distinct values: $\lambda=0,3$. Sum $=3$.