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MathsJEE Main 21 Jan 2026, Shift 2·Q14·MCQ·Moderate

Matrices & Determinants · Powers of a matrix

For the matrices A=[3−41−1]andB=[−2949−1318],A = \begin{bmatrix} 3 & -4\\ 1 & -1\end{bmatrix} \quad\text{and}\quad B = \begin{bmatrix} -29 & 49\\ -13 & 18\end{bmatrix}, if (A15+B)[xy]=[00](A^{15} + B)\begin{bmatrix} x\\ y\end{bmatrix} = \begin{bmatrix} 0\\ 0\end{bmatrix}, then among the following which one is true?
  1. (1)x=5x = 5, y=7y = 7
  2. (2)x=18x = 18, y=11y = 11
  3. (3)x=11x = 11, y=2y = 2
  4. (4)x=16x = 16, y=3y = 3

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