assig8M235W08 - Math 235 Linear Algebra II Assignment 8 Due...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 235 Linear Algebra II Assignment 8 Due 9:30am, Wednesday Nov 12, 2008, in the drop box designated for your section. 1. Let W be the subspace of R 4 spanned by (1 , ,- 1 , 2) and (2 , 1 , ,- 1) and take the inner product to be the dot product. (a) Find the dimension of W . (b) Find the vector in W which is closest to the vector (4 , 3 , 2 , 1). (c) Find a basis for W . (d) Find the unique w 1 W and w 2 W such that (4 , 3 , 2 , 1) = w 1 + w 2 . 2. Consider the real vector space C [0 , 1] of continuous functions on inter- val [0 , 1] together with the inner product given by < f,g > = R 1 f ( t ) g ( t ) dt for f,g C [0 , 1]. Let P 2 ( R ) be subspace of C [0 , 1] having a basis given by B = { 1 ,x,x 2 } . Find the best quadratic approximation to x on [0 , 1], i.e. find the best approximation to x by elements of P 2 ( R ). 3. Find the least-squares approximation to a solution of Ax = b by con- structing the normal equations for x and then solving for...
View Full Document

Page1 / 3

assig8M235W08 - Math 235 Linear Algebra II Assignment 8 Due...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online