ps7 - Problem Set 7 Math 115A/5 — Fall 2011 Due Monday...

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: Problem Set 7 Math 115A/5 — Fall 2011 Due: Monday, November 28 Please note a typo was corrected in problem 2. Problem 1 (5.2.3) For each of the following linear operators T on a vector space V , test T for diagonalizability, and if T is diagonalizable, find a basis β for V such that [ T ] β is a diagonal matrix. (a) V = P 3 ( R ) and T is defined by T ( f ( x )) = f ( x ) + f 00 ( x ). (b) V = P 2 ( R ) and T is defined by T ( ax 2 + bx + c ) = cx 2 + bx + a . (c) V = R 3 and T is defined by T a 1 a 2 a 3 = a 2- a 1 2 a 3 . (d) V = P 2 ( R ) and T is defined by T ( f ( x )) = f (0) + f (1)( x + x 2 ). (e) V = C 2 and T is defined by T ( z,w ) = ( z + iw,iz + w ). (f) V = M 2 × 2 ( R ) and T is defined by T ( A ) = A t . Problem 2 (5.2.7) For A = 1 4 2 3 ∈ M 2 × 2 ( R ) , find an expression for A n , where n is an arbitrary positive integer. (Hint: computing A n is easy when A is diagonal)....
View Full Document

This note was uploaded on 04/09/2012 for the course MATH 172a taught by Professor Kong,l during the Fall '08 term at UCLA.

Page1 / 2

ps7 - Problem Set 7 Math 115A/5 — Fall 2011 Due Monday...

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