ps8 - Problem Set 8 Math 115A/5 Fall 2011 Due: Friday,...

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

View Full Document Right Arrow Icon
Problem Set 8 Math 115A/5 — Fall 2011 Due: Friday, December 2 Problem 1 (6.2.2) In each part, apply the Gram-Schmidt process to the given subset S of the inner product space V to obtain an orthogonal basis for span( S ). Then normalize the vectors in the basis to obtain an orthonormal basis β for span( S ), and compute the Fourier coefficients of the given vector relative to β . (c) V = P 2 ( R ), with inner product h f ( x ) ,g ( x ) i = R 1 0 f ( t ) g ( t ) dt , S = { 1 ,x,x 2 } , and h ( x ) = 1 + x . (d) V = span( S ), where S = { (1 ,i, 0) , (1 - i, 2 , 4 i ) } , and x = (3 + i, 4 i, - 4). (g) V = M 2 × 2 ( R ), S = ±² 3 5 - 1 1 ³ , ² - 1 9 5 - 1 ³ , ² 7 - 17 2 - 6 ³´ , and A = ² - 1 27 - 4 8 ³ . Problem 2 (6.2.4) Let S = { (1 , 0 ,i ) , (1 , 2 , 1) } in C 3 . Compute S . Problem 3 (6.2.6) Let V be an inner product space, and let W be a finite-dimensional subspace of V . If x / W , prove that there exists y V such that y W , but h x,y i 6 = 0. Problem 4
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

ps8 - Problem Set 8 Math 115A/5 Fall 2011 Due: Friday,...

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