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MHT CET202616 April 2026Evening ShiftMathematicsMatricesActual

If A = bmatrix 2 & -1 0 & 2 bmatrix and A^2 + xA + yI₂ = O₂ , where I₂ and O₂ are the identity matrix and null matrix of order 2 respectively, then:

Options

  1. Ax = 4, y = 4
  2. Bx = -4, y = 4
  3. Cx = -4, y = -2
  4. Dx = 4, y = -4

Correct answer

B. x = -4, y = 4

Step-by-step solution

A^2 = bmatrix 2 & -1 0 & 2 bmatrix bmatrix 2 & -1 0 & 2 bmatrix = bmatrix 4 & -4 0 & 4 bmatrix Substituting A^2 , A , and I₂ into the given equation A^2 + xA + yI₂ = O₂ : bmatrix 4 & -4 0 & 4 bmatrix + x bmatrix 2 & -1 0 & 2 bmatrix + y bmatrix 1 & 0 0 & 1 bmatrix = bmatrix 0 & 0 0 & 0 bmatrix bmatrix 4 + 2x + y & -4 - x 0 & 4 + 2x + y bmatrix = bmatrix 0 & 0 0 & 0 bmatrix Equating the corresponding elements to zero: -4 - x = 0 x = -4 4 + 2x + y = 0 Substituting x = -4 into the second equation: 4 + 2(-4) + y = 0 y

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