Question
If M = 5 2 3 2 - 3 2 - 1 2 , then which of the following matrices is equal to M 2022 ?
JEE Advanced
Mathematics
Matrices
2022
JEE Advanced 2022 (Paper 2)
JEE Advanced Mathematics Question (2022) — Solution
Options
- A. 3034 3033 - 3033 - 3032
- B. 3034 - 3033 3033 - 3032
- C. 3033 3032 - 3032 - 3031
- D. 3032 3031 - 3031 - 3030
Answer
A. 3034 3033 - 3033 - 3032
Step-by-step solution
Given M = 5 2 3 2 - 3 2 - 1 2 M 2 = 5 2 3 2 - 3 2 - 1 2 5 2 3 2 - 3 2 - 1 2 = 4 3 - 3 - 2 M 3 = 5 2 3 2 - 3 2 - 1 2 4 3 - 3 - 2 = 11 2 9 2 - 9 2 - 7 2 M 4 = 11 2 9 2 - 9 2 - 7 2 11 2 9 2 - 9 2 - 7 2 = 7 6 - 6 - 5 and so on i.e. M n = 3 n 2 + 1 3 n 2 - 3 n 2 - 3 n 2 + 1 Hence, M 2022 = 3 × 2022 2 + 1 3 × 2022 2 - 3 × 2022 2 - 3 × 2022 2 + 1 = 3034 3033 - 3033 - 3032
Related: Mathematics — Matrices · All PYQ Banks