Q86.Let A = [ 21 −11 ] . If the sum of the diagonal elements of A13 is 3n , then n is equal to_________
What This Question Tests
This question requires finding the sum of diagonal elements (trace) of a high power of a matrix. It can be solved using eigenvalues, Cayley-Hamilton theorem, or by finding a pattern in matrix powers.
Concepts Tested
Formulas Used
Characteristic equation of a matrix A: det(A - λI) = 0
Trace of A^n = sum of (λ_i)^n
📚 NCERT Sections This Tests
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📋 Question Details
- Chapter
- Matrices
- Topic
- Powers of a matrix and Cayley-Hamilton Theorem
- Year
- 2024
- Shift
- 08 Apr Shift 1
- Q Number
- Q86
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 3: Matrices
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