This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 1 Homework 6 1. let V = R 2 . none of the the following are innerproducts. for each one, give, with explanation, an axiom which is violated. a. ( u,v ) = u 1 v 1 u 2 v 2 b. ( u,v ) = u 1 v 1 + u 2 v 1 + u 2 v 2 c. ( u,v ) = 0 d. ( u,v ) = u 1 v 2 5. 2. let V = C 3 , with the innerproduct ( u,v ) = u 1 v 1 + 2 u 2 v 2 + u 3 v 3 , and let U = span { (1 , , 1) , (1 ,i, 0) } V . find an orthonormal basis of U using gramschmidt. 3. let V = f : [0 , 2 ] R f is continuous , the vector space of all continuous realvalued functions on the interval [0 , 2 ], and define an innerproduct by ( f,g ) = Z 2 f ( x ) g ( x ) dx. let U be the threedimensional subspace spanned by U = span { 1 , sin , cos } . a. show that { 1 , sin , cos } are an orthogonal basis of U . find and orthonormal basis. b. let f V be the function f ( x ) = x x 2  x < x 2 1 which looks like a tent. find the projection proj U ( f ) of f onto U , and plot a couple points. is it pretty close tocouple points....
View Full
Document
 Spring '11
 Carlsson
 Linear Algebra, Algebra

Click to edit the document details