Mathematics · 2026
JEE Main · 21 January 2026, Shift 2 · Q5
For the matrices A = [3, -4; 1, -1] and B = [-29, 49; -13, 18], if ( A^15+ B ) [x; y] = [0; 0], then among the following which one is true?
For the matrices $\displaystyle \mathrm{A}=\left[\begin{array}{ll}3 & -4 \\ 1 & -1\end{array}\right]$ and $\displaystyle \mathrm{B}=\left[\begin{array}{ll}-29 & 49 \\ -13 & 18\end{array}\right]$, if $\displaystyle \left(\mathrm{A}^{15}+\mathrm{B}\right)\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{l}0 \\ 0\end{array}\right]$, then among the following which one is true ?
Official answer
From NTA’s final answer key for this paper.
(1)
$\displaystyle x=11, y=2$
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JEE Main 2026 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.