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Chapter 7: Q26E (page 372)

Find all complex eigenvalues of the matrices in Exercises 20 through 26 (including the real ones, of course). Do not use technology. Show all your work.

[1111111100110011]

Short Answer

Expert verified

The solution for all complex eigenvalues is 位1,2=1卤i,位3=0,位4=2.

Step by step solution

01

Define eigenvalue

Eigenvalues are a set of specialized scales associated with a system of linear equations. The corresponding eigenvalue, often denoted by位.

02

Find all complex eigenvalues

Consider the equation det(A-位I)=0,

1-位-11-111-位11001-位10011-位=01-位2=-1,1-位2=1=0

1-位2=-1,1-位2=11-位1,2=卤i,1-位3,4=卤1

So the complex eigenvalues is 位1,2=1卤i,位3=0,位4=2.

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