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If A is a 2 2 matrix such that det A=-21 and trace of A ^3 is 2024 , then the trace of A is

Options

  1. A6
  2. B11
  3. C12
  4. D13

Correct answer

B. 11

Step-by-step solution

Let eigen values of matrices A are ₁, ₁ ₁, ₂=-21 Eigen values of matrices A ^3 are ₁ ^3, ₂ ^3 Now ₁^3, ₂ ^3= ( ₁+ ₂ ) ( ₁ ^2+ ₂- ₁ ₂ ) 2024= ( ₁+ ₂ ) [ ₁^2+ ₂^2+21 ) 2024= ( ₁+ ₂ ) [ ( ₁+ ₂ )^2-2 ₁ ₂+21 ] 2024= ( ₁+ ₂ )^3-2 ₁ ₂ ( ₁+ ₂ )+21 ( ₁+ ₂ ) ( ₁+ ₂ )^3+63 ( ₁+ ₂ )-2024=0 (A) Here option (b) satisfied the given eq ^ n . (A) other options are not satisfied. ₁+ ₂= trace of A =11 .

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