Solveeit Logo
Login

Question

Question: The system of equations 6x + 5y + lz = 0, 3x – y + 4z = 0, x + 2y –3z = 0 has non-trivial solutions...

The system of equations 6x + 5y + lz = 0, 3x – y + 4z = 0,

x + 2y –3z = 0 has non-trivial solutions for

A

l = 0

B

l = 1

C

l = –5

D

None of these

Answer

l = –5

Explanation

Solution

For non-trivial solution D = 0

∣65λ3−1412−3∣\left| \begin{matrix} 6 & 5 & \lambda \\ 3 & - 1 & 4 \\ 1 & 2 & - 3 \end{matrix} \right|= 0

Ž –30 + 65 + 7l = 0 Ž l = –5