C__DOCUME~1_MAXWID~1_LOCALS~1_Temp_plugtmp-27_notes4-2

# C__DOCUME~1_MAXWID~1_LOCALS~1_Temp_plugtmp-27_notes4-2 -...

This preview shows pages 1–4. Sign up to view the full content.

SECTION 4.2 IMPORTANT EXAMPLES OF SUBSPACES A matrix A generates two subspaces. 1. The null space of A is the set of all solutions of A x = 0 , written as Nul A . 2. The column space of A is the span of the columns of A , written as Col A . Are these things really subspaces, and if so, of what exactly? Nul A Col A

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Closely related to Nul A and Col A are two subspaces generated by a linear transforma- tion. We can now talk about a linear transformation T from a vector space V to a vector space W . What does this mean? The kernel or null space of a linear transformation T is the set of all vectors u for which T ( u ) = 0 . The range of a linear transformation T is the set of all images of T , that is, the set of

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: all T ( x )’s. EXAMPLES (1) Find an explicit description of Nul 1 3 0-2 0 0 0 1-4 0 0 0 0 0 1 (2) Why is p q r : 3 p + 2 q = 5 r a subspace and what kind of subspace is it, exactly? (3) Why is p q r : 3 p + 2 q = 5 r + 1 not a subspace? (4) For A = 1 0-2 0 0 1-4 0 0 0 0 1 , where do Nul A and Col A live? Find nonzero vectors in each. HOMEWORK: SECTION 4.2...
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.

### Page1 / 4

C__DOCUME~1_MAXWID~1_LOCALS~1_Temp_plugtmp-27_notes4-2 -...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online