problem1 - EE221A Linear System Theory Problem Set 1...

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: 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.

Page1 / 2

problem1 - EE221A Linear System Theory Problem Set 1...

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