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Question

Find the sum of all real values of r for which the following system of linear equations has a non-trivial solution.
2rx2y+3z=0
x+ry+2z=0
2x++rz=0

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Solution

Given a system of equations has a non-trivial solution.
Δ=∣ ∣2r231r220r∣ ∣=0
2r3+2(r4)6r=0
r32r4=0
(r2)(r2+2r+2)=0
one root is real, and the remaining two are imaginary.
r=2
Sum of real values of r =2

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