Engineering Board Exam Reviewer · Eigenvalues and Eigenvectors · medium

A matrix A has eigenvalues 2 and 3. Find the eigenvalues of A2-3A+I.

1. 1 and 3
2. 4 and 9
3. -1 and 1
4. -1 and 3

Answer

C. -1 and 1

Solution

If Av= v then (A2-3A+I)v=( 2-3 +1)v. For =2: 4-6+1=-1. For =3: 9-9+1=1.

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