Name:Thursday section time:Student ID:Math 20F - Linear Algebra - Spring 2003Answers for Self-assessment Quiz #6.5 — June 51.LetAbe the matrixA=111022005.Answer the following questions: What are the eigenvalues ofA?Foreach eigenvalue, what is the the dimension of its eigenspace?IsAdiagonalizable? IsAdefective?ANSWER: These questions can be answered without having to do anyhard calculations. SinceAis triangular, its eigenvalues are the diagonalentries,λ1=1,λ2=2,λ3=5. Since the eigenvalues are distinct, eacheigenspace has dimension 1,Ais diagonalizable andAis not defective.2.Now letA=020-305. Find all ofA’s eigenvalues and eigenvectors.ANSWER: To ﬁnd the eigenvalues, we have
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This note was uploaded on 04/23/2008 for the course MATH 20F taught by Professor Buss during the Spring '03 term at UCSD.