Engineering Board Exam Reviewer · Eigenvalues and Eigenvectors · hard

Find the trace of A5 if A= bmatrix1&2\2&1 bmatrix.

1. 244
2. 32
3. 10
4. 242

Answer

D. 242

Solution

The eigenvalues of A are the roots of (1- )2-4=0: =3,-1. The eigenvalues of A5 are 35=243 and (-1)5=-1, and the trace is their sum: 243-1=242.

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