This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: FACT 3. If H is any subspace of a ﬁnitedimensional vector space V , then any set of linearly independent vectors in H can be extended to a basis for H , H is ﬁnitedimensional and dim H ≤ dim V . FACT 4. If we already know that dim V = p , then (1) any set of p linearly independent vectors is a basis for V , and (2) any set of p vectors that span V is a basis for V . EXAMPLE. Find the dimensions of Nul A and Col A when A = 12 47 0 9 1 2 5 1 0 0 0 13 2 0 0 0 1 0 0 0 0 . FACT 5. The dimension of Nul A is the number of free variables in the equation A x = , and the dimension of Col A is the number of pivot columns in A . EXAMPLE. Show that the ﬁrst four Hermite polynomials 1, 2 t ,2 + 4 t 2 , and12 t + 8 t 3 form a basis for P 3 . HOMEWORK: SECTION 4.5...
View
Full
Document
This note was uploaded on 04/15/2008 for the course M 340L taught by Professor Pavlovic during the Spring '08 term at University of Texas.
 Spring '08
 PAVLOVIC
 Linear Algebra, Algebra, Equations, Vectors, Sets

Click to edit the document details