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?

Correct answer: C. x=11, y=2 Here A^n = bmatrix 2n+1 & -4n n & -2n+1 bmatrix A^ 15 = bmatrix 31 & -60 15 & -29 bmatrix A^ 15 + B = bmatrix 2 & -11 2 & -11 bmatrix Now (A^ 15 + 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 .

JEE Main 202621 JanuaryEvening Shift

Exam: JEE Main
Year: 2026
Date: 21 January
Shift: Evening Shift
Subject: Mathematics
Chapter: Matrices

JEE Main 2026 · 21 January · Evening Shift · Mathematics · Matrices

For the matrices A=[ array ll 3 & -4 1 & -1 array ] and B=[ array...

For the matrices

\mathrm{A}=\left[

\begin{array}{ll}3 & -4 \\ 1 & -1\end{array}

\right] and

\mathrm{B}=\left[

\begin{array}{ll}-29 & 49 \\ -13 & 18\end{array}

\right]

, if

\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?

Options

A $x=5, y=7$
B $x=18, y=11$
C $x=11, y=2$
D $x=16, y=3$

Correct answer

C. $x=11, y=2$

Step-by-step solution

Here

A^n = \begin{bmatrix} 2n+1 & -4n \\ n & -2n+1 \end{bmatrix}

\Rightarrow A^{15} = \begin{bmatrix} 31 & -60 \\ 15 & -29 \end{bmatrix}

\Rightarrow A^{15} + B = \begin{bmatrix} 2 & -11 \\ 2 & -11 \end{bmatrix}

Now

(A^{15} + B) \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix}

\Rightarrow \begin{bmatrix} 2 & -11 \\ 2 & -11 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix}

\Rightarrow 2x - 11y = 0 \Rightarrow x = \frac{11y}{2}

.
For

y = 2

x = 11

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