DeterminantHard

Question

If a, b, c are non zeros, then the system of equations
        (α + a) x + αy + αz = 0
        αx + (α + b)y + αz = 0
        αx + αy + (α + c)z = 0
has a non-trivial solution if

Options

A.α-1 = - (a-1 + b-1 + c-1)
B.α-1 = a  + b + c
C.α  a + a + b + c = 1
D.none of these

Solution

For non-trivial solution
= 0
Taking a as common from each row
⇒  α3 = 0
Applying C1 → C1 - C3, C2 → C2 - C3 and expanding
⇒  α3 = 0
⇒ 

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