Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am having trouble understanding how to implement the four fundamental subspaces. I have read about the subject and understand the meaning but do not understand how to implement it when asked in a question. Can someone help me better grasp this.

An example question would be:

For each Matrix, accurately sketch the four fundamental subspaces on two R^2 plots so that the orthogonal pairs of subspaces are plotted together. This is the grid picture:

  |1 2|      |1 0|
A=|3 6|    B=|3 0|

Thanks!

share|improve this question

1 Answer 1

OK, so start by finding the four fundamental subspaces. What are they?

share|improve this answer
    
So Im looking for the column space, null space, row space and left nullspace correct? –  user081608 Oct 25 '13 at 5:22
    
Yes. So, let's start with the column space. What is it for $A$? –  Robert Israel Oct 25 '13 at 6:46
    
Would the new matrix be rows [1 0] and [0 0]? –  user081608 Oct 25 '13 at 17:05
    
So we get C(A) = 1, C(A^T) = 1, Nullspace = x2[01], left Null = 1 –  user081608 Oct 25 '13 at 17:19
    
Column space is by definition the linear span of the columns. In the case of $A$, the second column is $2$ times the first, so the column space is the span of $\pmatrix{1\cr 3\cr}$. –  Robert Israel Oct 27 '13 at 2:03

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.