Q. 205.0( 1 Vote )

# Prove the following identities –(CBSE 2014)

Answer :

Let

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 the term (a + x + y + z) common from C1, we get

Applying R2 R2 – R1, we get

Applying R3 R3 – R1, we get

Expanding the determinant along C1, we have

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

Δ = (a + x + y + z)(a)(a)

Δ = a2(a + x + y + z)

Thus,

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