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