If a, b and
Given that Δ = 0.
We can write the determinant Δ as
Taking a, b and c common from C1, C2 and C3, we get
Recall that the value of a determinant remains same if we apply the operation Ri→ Ri + kRj or Ci→ Ci + kCj.
Applying C1→ C1 + C2, we get
Applying C1→ C1 + C3, we get
Taking common from C1, we get
Applying R2→ R2 – R1, we get
Applying R3→ R3 – R1, we get
Expanding the determinant along C1, we have
We have Δ = 0.
It is given that a, b and c are all non-zero.
Thus, when and a, b, c are all non-zero.
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