Find the basis for the row space

  • Thread starter mottov2
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  • #1
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Homework Statement



Find the basis for the row space

The Attempt at a Solution



the given matrix is

0 1 2 1
2 1 0 2
0 2 1 1

So i reduced to row-echeleon form

2 1 0 2
0 1 2 1
0 0 3 1

so then rank = 3. My textbook states that the basis of the row space are the row vectors of leading ones, hence the basis for row space is
{ [2,1,0,2], [0,1,2,1], [0,0,3,1] }

however my textbook has this answer
{ [6,0,0,5], [0,3,0,1]. [0,0,3,1] }

HOW?!!?!?!!?!?! :-(

edit: NVM figured it out. Didnt realize the textbook reduced the matrix to reduced row form.
 
Last edited:

Answers and Replies

  • #2
lanedance
Homework Helper
3,304
2
also worth noting any linearly independent set of vectors that spans the space is a basis. In general there is no unique basis
 

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