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BITSAT2024MathematicsMatricesActual

If matrix A= [ array ccc 3 & -2 & 4 1 & 2 & -1 0 & 1 & 1 array ] and A⁻¹= 1 k adj (A) , then k is

Options

  1. A7
  2. B-7
  3. C15
  4. D-11

Correct answer

C. 15

Step-by-step solution

Given, A= [ array ccc 3 & -2 & 4 1 & 2 & -1 0 & 1 & 1 array ] and A⁻¹= 1 k adj (A) ....(i) We know that, A⁻¹= adj (A) |A| ...(ii) By comparing Eqs. (i) and (iii), k=|A| So, aligned |A| & = | array ccc 3 & -2 & 4 1 & 2 & -1 0 & 1 & 1 array | & =3(2+1)+2(1+0)+4(1-0)=15 aligned

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