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In this lesson, we will learn how to determine the eigenvalues of a nonzero square matrix by finding the scalar values that satisfy its characteristic equation.

Q1:

Can a real 3 Γ 3 matrix which has a nonreal eigenvalue be defective?

Q2:

Suppose that π , π£ is an eigenpair of the invertible matrix π΄ . Then 1 π , π£ is an eigenpair of which of the following matrices?

Q3:

Fill in the blanks.

Let π΄ be an π Γ π matrix. Then t r a c e ( π΄ ) equals and d e t ( π΄ ) equals .

Q4:

Is it possible for a nonzero matrix to have 0 as its only eigenvalue?

Q5:

Calculate the eigenvalues of

Q6:

Suppose π β πΏ ( π , π ) is a linear operator. Then π β πΉ is an eigenvalue of π if and only if

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