Q. 195.0( 1 Vote )

# Prove the following identities –(CBSE 2014)

Let

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

Applying R1 R1 + R2, we get

Applying R1 R1 + R3, we get

Taking the term (x + y + z) common from R1, we get

Applying C2 C2 – C1, we get

Applying C3 C3 – C1, we get

Expanding the determinant along R1, we have

Δ = (x + y + z)(1)[0 – (–(x + y + z)(x + y + z))]

Δ = (x + y + z)(x + y + z)(x + y + z)

Δ = (x + y + z)3

Thus,

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