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JEE Main202621 January 2026Evening ShiftMathematicsMatricesActual

For the matrices A = [ array ll 3 & -4 1 & -1 array ] and B = [ array ll -29 & 49 -13 & 18 array ] , if ( A ¹⁵+ B ) [ array l x y array ]= [ array l 0 0 array ] , then among the following which one is true?

Options

  1. Ax=5, y=7
  2. Bx=18, y=11
  3. Cx=11, y=2
  4. Dx=16, y=3

Correct answer

C. x=11, y=2

Step-by-step solution

Here A^n = bmatrix 2n+1 & -4n n & -2n+1 bmatrix A¹⁵ = bmatrix 31 & -60 15 & -29 bmatrix A¹⁵ + B = bmatrix 2 & -11 2 & -11 bmatrix Now (A¹⁵ + B) bmatrix x y bmatrix = bmatrix 0 0 bmatrix bmatrix 2 & -11 2 & -11 bmatrix bmatrix x y bmatrix = bmatrix 0 0 bmatrix 2x - 11y = 0 x = 11y 2 . For y = 2 , x = 11 .

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