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Let A = bmatrix & 1 & 2 2 & 3 & 0 0 & 4 & 5 bmatrix and B = bmatrix 1 & 0 & 0 0 & -5 & 0 0 & 4 & -2 bmatrix + adj (A) . If (B)=66 , then ( adj (A)) equals:

Options

  1. A289
  2. B361
  3. C441
  4. D529

Correct answer

C. 441

Step-by-step solution

The cofactor matrix of A is calculated as follows: C₁₁ = 15 , C₁₂ = -10 , C₁₃ = 8 C₂₁ = 3 , C₂₂ = 5 , C₂₃ = -4 C₃₁ = -6 , C₃₂ = 4 , C₃₃ = 3 - 2 The adjoint of A is the transpose of the cofactor matrix: adj (A) = bmatrix 15 & 3 & -6 -10 & 5 & 4 8 & -4 & 3 - 2 bmatrix The matrix B is given by: B = bmatrix 1 & 0 & 0 0 & -5 & 0 0 & 4 & -2 bmatrix + bmatrix 15 & 3 & -6 -10 & 5 & 4 8 & -4 & 3 - 2 bmatrix = bmatrix 16 & 3 & -6 -10 & 0 & 4 8 & 0 & - 2 bmatrix Expanding the determinant of B along the second column: (B) = -3

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