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MHT CET202613 April 2026Evening ShiftMathematicsMatricesActual

The element in 1st row and 2nd column of the inverse of the matrix bmatrix 1 & 3 & -2 -3 & 0 & -5 2 & 5 & 0 bmatrix is ...

Options

  1. A- 2 5
  2. B- 10 3
  3. C- 2 25
  4. D1 25

Correct answer

A. - 2 5

Step-by-step solution

Let A = bmatrix 1 & 3 & -2 -3 & 0 & -5 2 & 5 & 0 bmatrix The determinant of A is given by: |A| = 1(0 - (-25)) - 3(0 - (-10)) - 2(-15 - 0) |A| = 25 - 30 + 30 = 25 The inverse of matrix A is A⁻¹ = 1 |A| adj (A) . The element in the 1st row and 2nd column of A⁻¹ is 1 |A| C₂₁ , where C₂₁ is the cofactor of the element a₂₁ in A . C₂₁ = (-1)²⁺¹ vmatrix 3 & -2 5 & 0 vmatrix = -(0 - (-10)) = -10 Therefore, the required element is -10 25 = - 2 5 .

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