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Chapter 7: Q23E (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.

23)|001100010|

Short Answer

Expert verified

位1=1,位2,3=-1卤3i2

Step by step solution

01

Define eigen values

The scalar values correlated to the system of linear equations, mostly comprising of matrix are called eigen values.

02

Find complex eigenvalues of the matrices

If the n 脳 n matrix A has real entries, its complex eigenvalues will always occur in complex conjugate pairs.

Solve,

det(A-位濒)=0-位011-位001-位=0-位3+1=0位3-1=0det(A-位濒)=0位1=1,位2,3=-1卤1-42=-1卤3i2

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Most popular questions from this chapter

7:For each of the matrices in Exercises 1 through 13, find all real eigenvalues, with their algebraic multiplicities. Show your work. Do not use technology.

l3

In all parts of this problem, let V be the linear space of all 2 脳 2 matrices for which [12]is an eigenvector.

(a) Find a basis of V and thus determine the dimension of V.

(b) Consider the linear transformation T (A) = A[12] from V to R2. Find a basis of the image of Tand a basis of the kernel of T. Determine the rank of T .

(c) Consider the linear transformation L(A) = A[13] from V to R2. Find a basis of the image of L and a basis of the kernel of L. Determine the rank of L.

For each of the matrices in Exercises 1 through 13, find all real eigenvalues, with their algebraic multiplicities. Show your work. Do not use technology.

[04-14]

Find a basis of the linear space Vof all3脳3matrices Afor which both[100]and[001]are eigenvectors, and thus determine the dimension of.

Consider the coyotes鈥搑oadrunner system discussed in Example 7. Find closed formulas for c(t) and r(t), for the initial populations c0= 100, r0 = 800.
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