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If A = 1 1 0 2 1 5 1 2 1 , then a 11 A 21 + a 12 A 22 + a 13 A 23 = _______

Options

  1. A1
  2. B0
  3. C- 1
  4. D2

Correct answer

B. 0

Step-by-step solution

Here, a i j stands for element of matrix A in i t h row and j t h column, and A i j stands for co-factor of element a i j of matrix A . ∴ a 11 = 1 , a 12 = 1 , a n d a 13 = 0 And A 21 = - 1 2 + 1 1 0 2 1 = - 1 A 22 = - 1 2 + 2 1 0 1 1 = 1 A 23 = - 1 2 + 3 1 1 1 2 = - 1 Therefore a 11 A 21 + a 12 A 22 + a 13 A 23 = 1 × - 1 + 1 × 1 + 0 × - 1 = 0

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