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 2011 Issued 9/1; Due 9/8 Problem 1: Functions. Consider f : R 3 R 3 , defined as f ( x ) = Ax,A = 1 1 1 1 ,x R 3 Is f a function? Is it injective? Is it surjective? Justify your answers. Problem 2: Fields. (a) Use the axioms of the field to show that, in any field, the additive identity and the multiplicative identity are unique. (b) Is GL n , the set of all n n nonsingular matrices, a field? Justify your answer. Problem 3: Vector Spaces. (a) Show that ( R n , R ), the set of all ordered ntuples of elements from the field of real numbers R , is a vector space. (b) Show that the set of all polynomials in s of degree k or less with real coefficients is a vector space over the field R . Find a basis. What is the dimension of the vector space?...
View Full
Document
 Fall '10
 ClaireTomlin
 Electrical Engineering

Click to edit the document details