Question
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?
JEE Main
Mathematics
Matrices
2026
JEE Main 2026 (21 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. x=5, y=7
- B. x=18, y=11
- C. x=11, y=2
- D. x=16, y=3
Answer
C. x=11, y=2
Step-by-step solution
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.
Related: Mathematics — Matrices · All PYQ Banks