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MHT CET202618 April 2026Evening ShiftMathematicsMatricesActual

Let A = bmatrix -3 & 2 1 & 4 bmatrix and if A^2 - 2A + I = bmatrix 18 & p q & 11 bmatrix , then

Options

  1. Ap = -2, q = -1
  2. Bp = 2, q = 1
  3. Cp = -1, q = -2
  4. Dp = 1, q = 2

Correct answer

A. p = -2, q = -1

Step-by-step solution

Given A = bmatrix -3 & 2 1 & 4 bmatrix First, we calculate A^2 : A^2 = bmatrix -3 & 2 1 & 4 bmatrix bmatrix -3 & 2 1 & 4 bmatrix = bmatrix 9 + 2 & -6 + 8 -3 + 4 & 2 + 16 bmatrix = bmatrix 11 & 2 1 & 18 bmatrix Next, we calculate 2A : 2A = 2 bmatrix -3 & 2 1 & 4 bmatrix = bmatrix -6 & 4 2 & 8 bmatrix Now, substituting these into A^2 - 2A + I : A^2 - 2A + I = bmatrix 11 & 2 1 & 18 bmatrix - bmatrix -6 & 4 2 & 8 bmatrix + bmatrix 1 & 0 0 & 1 bmatrix = bmatrix 11 - (-6) + 1 & 2 - 4 + 0 1 - 2 + 0 & 18 - 8 + 1 bmatrix =

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