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Chapter 7: Q21E (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.

21)[11-156-7]

Short Answer

Expert verified

位1,2=2卤3i

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)=011-位-156-7-位=011-位-7-位+90=0位2-4位+13=0位2+4+16-522=2卤3i

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Most popular questions from this chapter

Arguing geometrically, find all eigen vectors and eigen values of the linear transformations. In each case, find an eigen basis if you can, and thus determine whether the given transformation is diagonalizable.

Scaling by 5 inR3.

Consider ann脳n matrix such that the sum of the entries in each row is . Show that the vector

e鈫�=11..1

InRn is an eigenvector of A. What is the corresponding eigenvalue?

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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]

Is v鈬赌an eigenvector of 7 A? If so, what is the eigenvalue?
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