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Unformatted text preview: 2 ) = ( a + b, 2 c,ab ) . Let β and γ be the standard ordered bases for P 2 ( R ) and R 3 , respectively. (a) Compute [ U ] γ β , [ T ] β , and [ UT ] γ β directly. Verify your results with Theorem 2.11. (b) Let h ( x ) = 32 x + x 2 . Compute [ h ( x )] β and [ U ( h ( x ))] γ . Verify your results with Theorem 2.14. 1 8. (4%+4%) Problem 13 of Section 2.3. 9. (4%+6%) (a) Show that T : R 3 → R 3 deFned by T ( a 1 ,a 2 ,a 3 ) = (3 a 12 a 3 ,a 2 , 3 a 1 +4 a 2 ) is invertible. (b) Let A and B be n × n invertible matrices. Prove that AB is invertible and ( AB ) − 1 = B − 1 A − 1 . 10. (6%+6%) Problem 17 of Section 2.4. [Moved to HW#3] 2...
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 Spring '11
 EE
 Linear Algebra, Vector Space, 5%, 4%

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