This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 205, Spring 2011 Homework 7: due March 14 Chapter 4, Sections 6, 8 and 10 (Review, T/F Questions) Week 7: 4.6 Bases and Dimension 4.8 Row and Column Space 4.10 Invertible Matrices (Review) ———– 2 Bases and Dimension Our main objective is the definition of basis. Vectors vectorv 1 ,vectorv 2 , . . . ,vectorv k in a vector space V that are are both (1) a spanning set for V and (2) linearly independent are called a basis for V. So (1) vector i, vector j are a basis of R 2 ; and (2) { vector i, vector j, vector k } is a basis of R 3 . A vector space has many bases, but the main fact is that if vectorv 1 ,vectorv 2 , . . . ,vectorv k is a basis of V and vectorw 1 , vectorw 2 , . . . , vectorw j is a second basis of V, then the number of vectors is the same: k = j. The number of vectors in a basis of V is called the dimension of V . 3 We start with verifications of linear independence in subspaces of R n Example: Show that the vectors vectorv 1 = (1 , 1) vectorv 2 = (1 , − 1) are a basis of...
View
Full Document
 Spring '08
 zhang
 Linear Algebra, Matrices, Vector Space, basis, main fact

Click to edit the document details