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MHT CET202616 April 2026Morning ShiftMathematicsMatricesActual

If A = bmatrix 5a & -b 3 & 2 bmatrix and A ,( adj A) = AA^T , Then 5a + b =

Options

  1. A2
  2. B3
  3. C5
  4. D15 2

Correct answer

C. 5

Step-by-step solution

Given A = bmatrix 5a & -b 3 & 2 bmatrix . Using the property A( adj A) = |A|I , the given equation becomes AA^T = |A|I . |A| = (5a)(2) - (-b)(3) = 10a + 3b AA^T = bmatrix 5a & -b 3 & 2 bmatrix bmatrix 5a & 3 -b & 2 bmatrix = bmatrix 25a^2 + b^2 & 15a - 2b 15a - 2b & 13 bmatrix Equating AA^T to |A|I : bmatrix 25a^2 + b^2 & 15a - 2b 15a - 2b & 13 bmatrix = bmatrix 10a + 3b & 0 0 & 10a + 3b bmatrix From the off-diagonal elements: 15a - 2b = 0 b = 15a 2 From the bottom-right elements: 10a + 3b = 13 Substituting b = 15a

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