Engineering Board Exam Reviewer · Eigenvalues and Eigenvectors · easy

A 2×2 matrix has eigenvalues 3 and -2. What are its determinant and trace?

1. =-6, trace=1
2. =1, trace=-6
3. =6, trace=1
4. =-6, trace=5

Answer

A. =-6, trace=1

Solution

The determinant is the product of the eigenvalues, 3(-2)=-6, and the trace is their sum, 3+(-2)=1.

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