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KCET2023MathematicsDeterminants

The value of | array lll ^2 14^ & ^2 66^ & 135^ ^2 66^ & 135^ & ^2 14^ 135^ & ^2 14^ & ^2 66^ array | is

Options

  1. A0
  2. B1
  3. C2
  4. D-1

Correct answer

A. 0

Step-by-step solution

Here, | array ccc ^2 14^ & ^2 66^ & 135^ ^2 66^ & 135^ & ^2 14^ 135^ & ^2 14^ & ^2 66^ array | Applying C₁ C₁+C₂+C₃= | array lll ^2 14^ + ^2 66^ + 135^ & ^2 66^ 135^ ^2 14^ + ^2 66^ + 135^ & 135^ ^2 14^ ^2 14^ + ^2 66^ + 135^ & ^2 14^ ^2 66^ array | aligned & = ^2 14^ + ^2 66^ + 135^ & | array lll 1 & ^2 66^ & 135^ 1 & 135^ & ^2 14^ 1 & ^2 14^ & ^2 66^ array | aligned = ^2 14^ + ^2 66^ -1 | array ccc 1 & ^2 66 & -1 1 & -1 & ^2 14^ 1 & ^2 14^ & ^2 66^ array | Applying R₁ R₁-R₂, R₂ R₂-R₃ aligned & = ^2 66^ + ^2 66^ -

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