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Kiran purchased 3 pencils, 2 notebooks and one pen for ₹41. From the same shop Manasa purchased 2 pencils, one notebook and 2 pens for ₹ 29, while Shreya purchased 3 pencils, 2 notebooks and 2 pens for ₹44. The above situation can be represented in matrix form as A X=B . Then | adj A| is equal to

Options

  1. A-1
  2. B1
  3. C-9
  4. D9

Correct answer

B. 1

Step-by-step solution

Coefficient matrix: A = bmatrix 3 & 2 & 1 2 & 1 & 2 3 & 2 & 2 bmatrix Applying R₃ R₃ - R₁ : |A| = vmatrix 3 & 2 & 1 2 & 1 & 2 0 & 0 & 1 vmatrix Expanding along R₃ : |A| = 1 (3 1 - 2 2) = 3 - 4 = -1 For a 3 3 matrix: | adj A| = |A|^ n-1 = |A|^2 = (-1)^2 = 1

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