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Chapter 7: Q25E (page 345)

What can you say about the geometric multiplicity of the eigenvalues of a matrix of the form

A=[010001abc]

Short Answer

Expert verified

For all eigenvalues 位appliesgemu(位)=1

Step by step solution

01

Step1:Definition of Kernal of a matrix transformation

A linear transformation's kernel, or null-space, is the set of all the vectors in the input space that are transferred to the null vector in the output space by the linear transformation.

if 位is an eigenvalue of A,

02

Find the linear is independent or dependent

Then

E位=kerA-位濒E位=ker-位100-位1abc-位

The last two rows of this matrix are linearly independent, so we have dimE位=1,thereforegemu位=1

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