Q. 235.0( 3 Votes )

If <i

Answer :

Let


Given that Δ = 0.


Recall that the value of a determinant remains same if we apply the operation Ri Ri + kRj or Ci Ci + kCj.


Applying R2 R2 – R1, we get




Applying R3 R3 – R1, we get




Expanding the determinant along C3, we have


Δ = (c – z)[0 – (–x)(y)] – 0 + z[(a)(y) – (–x)(b – y)]


Δ = (c – z)(xy) + z[ay + xb – xy]


Δ = cxy – xyz + ayz + bxz – xyz


Δ = ayz + bxz + cxy – 2xyz


We have Δ = 0


ayz + bxz + cxy – 2xyz = 0


ayz + bxz + cxy = 2xyz





Thus, when.

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