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If A = 5 a - b 3 2 and A . a d j A = A A T , then 5 a + b is equal to

Options

  1. A4
  2. B13
  3. C- 1
  4. D5

Correct answer

D. 5

Step-by-step solution

A = 5 a - b 3 2 and A T = 5 a 3 - b 2 A A T = 25 a 2 + b 2 15 a - 2 b 15 a - 2 b 13 Now, A . a d j A = A I 2 = 10 a + 3 b 0 0 10 a + 3 b Given A A T = A . a d j   A 15 a - 2 b = 0 ......(i) 10 a + 3 b = 13 .......(ii) Solving we get 5 a = 2 and b =   3 ∴ 5 a + b = 5

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