{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

problems-4-223-F07

# problems-4-223-F07 - M ATH 223 P ROBLEM S ET 4 D UE 2 O...

This preview shows page 1. Sign up to view the full content.

M ATH 223 P ROBLEM S ET 4 D UE : 2 O CTOBER 2007 When you hand in this problem set, please indicate on the top of the front page how much time it took you to complete. Reading. § 2.6, § 1.5&1.6. Problems from the book: the starred problems will be graded. 2.6.2, 2.6.3, 2.6.5, 2.6.8 , 2.6.9. 1.5.2 , 1.5.3, 1.5.7, 1.5.10, 1.5.18. 1.5.24 . Additional problems: 1. Are the following subsets of P ol 5 ( R ) subspaces? If so, find a basis and compute the dimension. (a) braceleftbig f ∈ P ol 5 ( R ) vextendsingle vextendsingle f (- x ) = - f ( x ) bracerightbig ; (b) braceleftbig f ∈ P ol 5 ( R ) vextendsingle vextendsingle f (- x ) = ( f ( x )) 2 bracerightbig ; and (c) braceleftbig f ∈ P ol 5 ( R ) vextendsingle vextendsingle f ( 2 ) = 0 bracerightbig . 2. Given a basis - v 1 ,,..., - v n of R n , the Gramm-Schmidt algorithm produces a new orthonormal basis. Prove that this new basis is orthonormal! - u 1 = - v 1 | - v 1 | , - u 2 = - v 2 - ( - v 2 · - u 1 ) - u 1 | - v 2 - ( - v 2 · - u 1 ) - u 1 | , . . . -
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Ask a homework question - tutors are online