Math416_ColumnNull - Math 416 - Abstract Linear Algebra...

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: Math 416 - Abstract Linear Algebra Fall 2011, section E1 Column space and null space The following example illustrates the notion of dimension and “culling down” a linearly depen- dent collection of vectors. Let A = a 1 a 2 a 3 = 1 2 1 2 4 1 3 6 1 1 2 1 . Find the dimension of Col A and Null A , as well as a basis for each. A = 1 2 1 2 4 1 3 6 1 1 2 1 ∼ 1 2 1 0 0- 1 0 0- 2 0 0 ∼ 1 2 1 0 0 1 0 0 0 0 0 0 ∼ 1 2 0 0 0 1 0 0 0 0 0 0 Since the pivots are in columns 1 and 3, we conclude dimCol A = 2 and a basis of Col A is given by { a 1 ,a 3 } = { 1 2 3 1 , 1 1 1 1 } . Remark 1: We have culled down the linearly dependent collection { a 1 ,a 2 ,a 3 } to a basis of Span { a 1 ,a 2 ,a 3 } = Col A . In other words, since a 2 is already in Span { a 1 ,a 3 } , we have...
View Full Document

This note was uploaded on 12/16/2011 for the course MATH 416 taught by Professor Frankland during the Fall '11 term at University of Illinois at Urbana–Champaign.

Page1 / 3

Math416_ColumnNull - Math 416 - Abstract Linear Algebra...

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