223 homework 6

223 homework 6 - Math 223, Section 102, Homework no. 6 (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 223, Section 102, Homework no. 6 (due Wednesday, October 27, 2010) [8 exercises, 35 points + 7 bonus points] Exercise 1 (6 points) . Consider the matrix A = 1 1 1 1 1 2 3 1- 1 2 2 1 0 1 ∈ M 4 × 4 ( R ) . (1) (3 points) Is A invertible? If yes, compute its inverse. Now consider the linear transformation T : P 3 ( R ) → P 3 ( R ) , f ( x ) 7→ f ( x + 1) + x 2 f (- 1) + x 3 f (0) . We use the standard ordered basis β = (1 ,x,x 2 ,x 3 ) for P 3 ( R ). (2) (1 point) Determine the matrix [ T ] β β . (3) (2 points) Is T invertible? If yes, give a formula for T- 1 ( f ) for arbitrary f ∈ P 3 ( R ). Exercise 2 (6 points + 2 bonus points) . Consider the linear transformation L A : R 2 → R 2 (see Assignment No. 5, Exercise 9) for the matrix A = 1 10 17 9 9- 7 . (1) (1 point) Let β = ( e 1 ,e 2 ) be the standard ordered basis for R 2 . Determine [ L A ] β β . (2) (3 points) Compute the matrices [ I R 2 ] β γ and [ I R 2 ] γ β for the ordered basis γ = 1 √ 10 3 1 , 1 √ 10- 1 3 ....
View Full Document

This note was uploaded on 09/30/2011 for the course MATH 221 at UBC.

Page1 / 3

223 homework 6 - Math 223, Section 102, Homework no. 6 (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