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: EE221A Linear System Theory Problem Set 1 Professor C. Tomlin Department of Electrical Engineering and Computer Sciences, UC Berkeley Fall 2007 Issued 9/4; Due 9/13 Problem 1: Fields. (a) Define addition and multiplication on { , 1 } to form a field. Show that your result is a field. (b) Use the axioms of the field to show that, in any field, the additive identity and the multiplicative identity are unique. Problem 2: Vector Spaces. Let R 2 2 be the set of all 2 2 real matrices. (a) Briefly verify that R 2 2 is a vector space under usual matrix addition and scalar multiplication. Dont turn this in. (b) What is the dimension of R 2 2 ? (c) Find a basis for R 2 2 . (d) Let A = bracketleftbigg 1 1 2 bracketrightbigg Is the set { I,A,A 2 } linearly dependent or independent in R 2 2 ? Problem 3: Subspaces. Consider the space F of all functions f : R + R , which have a Laplace transform f ( s ) = integraltext f ( t ) e st dt defined for all Re ( s ) > 0. For some fixed0....
View
Full
Document
This note was uploaded on 12/09/2011 for the course EE 221A taught by Professor Clairetomlin during the Fall '10 term at University of California, Berkeley.
 Fall '10
 ClaireTomlin
 Electrical Engineering

Click to edit the document details