Unformatted text preview: a) ; âŽ âŽ¬ âŽ« âŽ© âŽ¨ âŽ§ âŽ¥ âŽ¦ âŽ¤ âŽ¢ âŽ£ âŽ¡ âŽ¥ âŽ¦ âŽ¤ âŽ¢ âŽ£ âŽ¡ âŽ¥ âŽ¦ âŽ¤ âŽ¢ âŽ£ âŽ¡ âŽ¥ âŽ¦ âŽ¤ âŽ¢ âŽ£ âŽ¡ 1 , 1 1 1 , 1 1 , 1 1 b) {1 + x, x + x 2 , x 2 + x 3 , x 3 }. 2) Exhibit a basis of each of the following subspaces of the spaces indicated. a) {p(x)  p(x)= p( â€“ x)}; in P 2 . b) âŽª âŽ âŽª âŽ¬ âŽ« âŽª âŽ© âŽª âŽ¨ âŽ§ âŽ¥ âŽ¦ âŽ¤ âŽ¢ âŽ£ âŽ¡ = âŽ¥ âŽ¦ âŽ¤ âŽ¢ âŽ£ âŽ¡ âˆ’ 1 1 A A ; in M 22 . 3) Let A 0 and B â‰ 0 be n â‰ Ã— n matrices, and assume tat A is symmetric and B is skewsymmetric (that is, B T = â€“ B ). Show that the set {A, B} is independent. Note: There are answers at the back of the textbook for the odd number questions....
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 Spring '10
 X.Jiang
 Linear Algebra, Algebra, Vector Space, Fraleigh

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