Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Physical Sciences Mathematical Methods of Physics
Let A be a \(3 \times 3\) matrix with eigenvalues 2, -1, and 4. Which of the following is true based on the Cayley-Hamilton theorem?
A) \(A^3 - 5A^2 - 2A + 8 I = 0 \)
B) \(A^3 - 5A^2 + 2A + 8 I = 0 \)
C) \( A^3 - 5A^2 + 2A - 8 I = 0 \)
D) \(A^3 + 5A^2 - 2A -8 I= 0 \)
1
Only A
2
Only B
3
Only C
4
Both B and C
5
Question Not Attempted