Q. 75.0( 1 Vote )

Prove the followi

Answer :

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 (5x + 4) 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 = (5x + 4)[(1)(4 – x)(4 – x)]


Δ = (5x + 4)(4 – x)2


Thus,

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