Eigenvalues and Eigenvectors — Engineering Board Exam Practice Questions

8 free engineering board exam reviewer questions on Eigenvalues and Eigenvectors (Advanced Engineering Mathematics), each with the correct answer and a worked solution.

1. Find the trace of A5 if A= bmatrix1&2\2&1 bmatrix.
2. A matrix A has eigenvalues 2 and 3. Find the eigenvalues of A2-3A+I.
3. Find the largest eigenvalue of bmatrix2&0&0\0&3&4\0&4&9 bmatrix.
4. An eigenvector of bmatrix4&1\2&3 bmatrix corresponding to =5 is
5. Find the eigenvalues of bmatrix4&1\2&3 bmatrix.
6. Find the eigenvalues of bmatrix2&1\1&2 bmatrix.
7. A 2×2 matrix has eigenvalues 3 and -2. What are its determinant and trace?
8. Find the eigenvalues of bmatrix3&1\0&5 bmatrix.