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Unformatted text preview: ˜ ˜ . 4. (25) The matrix A = 1 14 4 2 21 1 ˆ ˜ ˜ ˜ has characteristic polynomial 1 t ( ) 2 t ( ) 2 . a. Find all eigenvalues and eigenvectors of A . b. Either find an invertible matrix S and a diagonal matrix D with S1 AS = D or explain why no such S and D exist. Name±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± Page 2 of 2 Math 1502J 2pm Andrew Hour Test 3 Teaching Assistant±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± 15 April 2004 Answers. 1. 1 3 ˆ ˜ 2. A basis for the kernel is 21 1 ˆ ˜ ˜ ˜ ˜ . A basis for the image consists of the pivot columns 1 2 1 1 ˆ ˜ ˜ ˜ ˜ , 3 1 1 ˆ ˜ ˜ ˜ ˜ , 4 2 ˆ ˜ ˜ ˜ ˜ 3. 21 4. a. l = 1 , 12 1 ˆ ˜ ˜ ˜ and = 2 , 1 2 ˆ ˜ ˜ ˜ , 1 2 ˆ ˜ ˜ ˜ b. S =1 1 12 2 1 2 ˆ ˜ ˜ ˜ D = 1 2 2 ˆ ˜ ˜ ˜...
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 Fall '07
 McClain
 Math, Linear Algebra, Teaching assistant, 2 hour, 1502J, 2004 Hour, Math 1502J

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