Topic: Linear Algebra
Given that the Eigen values of matrix A3x3 are 1, 3 and 5. The Eigen values of A³ are:
- A. 1, 3 and 5
- B. 3, 9 and 15
- C. 1, 27, 125
- D. Given information is inadequate
Answer: C. 1, 27, 125
Explanation: If $\lambda$ is an eigenvalue of a matrix $A$, then $\lambda^n$ is an eigenvalue of the matrix $A^n$. Given the eigenvalues of $A$ are 1, 3, and 5, the eigenvalues of $A^3$ will be $1^3, 3^3$, and $5^3$, which evaluate to 1, 27, and 125.