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Chapter 7: Q24E (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.

(0100015-73)

Short Answer

Expert verified

The solution for all complex eigenvalues is位1=1,位2,3=-1卤2i

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

  Step 2: Find all complex eigenvalues

Consider the equation detA-位濒=0,

-位100-位15-73-位=0位23-位+5-7位=0-位3+3位2-7位+5=0位-1-位2+2位-5=0位1=1位2,3=-2卤4-20-2

So the complex eigenvalues is位1=1,位2,3=-1卤2i

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