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Spring 2003 - Buss' Class - Quiz 6.5

# Spring 2003 - Buss' Class - Quiz 6.5 - Name Student ID...

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Name: Thursday section time: Student ID: Math 20F - Linear Algebra - Spring 2003 Answers for Self-assessment Quiz #6.5 — June 5 1. Let A be the matrix A = 111 022 005 . Answer the following questions: What are the eigenvalues of A ?F o r each eigenvalue, what is the the dimension of its eigenspace? Is A diagonalizable? Is A defective? ANSWER: These questions can be answered without having to do any hard calculations. Since A is triangular, its eigenvalues are the diagonal entries, λ 1 =1 , λ 2 =2 , λ 3 =5 . Since the eigenvalues are distinct, each eigenspace has dimension 1, A is diagonalizable and A is not defective. 2. Now let A = 020 - 305 . Find all of A ’s eigenvalues and eigenvectors. ANSWER: To ﬁnd the eigenvalues, we have
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