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Let A = x 2 - 3 - 1 3 - 2 2 - 1 1 be a matrix and a d j a d j A = 12 4 , then the sum of all the values of x is equal to

Options

  1. A- 24
  2. B24
  3. C- 18
  4. D1

Correct answer

C. - 18

Step-by-step solution

A = x 2 - 3 - 1 3 - 2 2 - 1 1 = x 1 - 2 3 - 3 - 5 = x + 9 a d j a d j A = A 4 (By property) ⇒ A 4 = 12 4 ⇒ A = ± 12 ⇒ x + 9 = ± 12 ⇒ x = 3 , - 21

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