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COMEDK20269 May 2026Evening ShiftMathematicsMatricesActual

Given A = bmatrix x & 1 & -2 bmatrix and B = bmatrix 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 bmatrix . If ABA^t = [-20] then the value of x is:

Options

  1. A1
  2. B-1
  3. C-3
  4. D11

Correct answer

D. 11

Step-by-step solution

A = bmatrix x & 1 & -2 bmatrix B = bmatrix 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 bmatrix AB = bmatrix x & 1 & -2 bmatrix bmatrix 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 bmatrix AB = bmatrix x(1) + 1(4) - 2(7) & x(2) + 1(5) - 2(8) & x(3) + 1(6) - 2(9) bmatrix AB = bmatrix x - 10 & 2x - 11 & 3x - 12 bmatrix ABA^t = bmatrix x - 10 & 2x - 11 & 3x - 12 bmatrix bmatrix x 1 -2 bmatrix ABA^t = [x(x - 10) + 1(2x - 11) - 2(3x - 12)] ABA^t = [x^2 - 10x + 2x - 11 - 6x + 24] ABA^t = [x^2 - 14x + 13] Given ABA^t = [-20] , we have: x^2 - 14x + 13

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