# How do I find the bases for row(A), col(A) and null(A)?

• Nov 25th 2010, 07:10 PM
s3a
How do I find the bases for row(A), col(A) and null(A)?
Given matrix A = ([1,0,-1],[1,1,1]), how do I find the bases for row(A), col(A) and null(A)?

I know this is very simple for you guys but I am struggling to keep up with my work load and would really appreciate it if someone could explain it to me.

Thanks!
• Nov 25th 2010, 11:27 PM
Roam
First you have to reduce your matrix to row echelon form. The nonzero rows of this reduced matrix form a basis for $row(A)$. What are they?

Now the columns of this reduced matrix wih leading 1's identify the pivot columns of your original matrix. And these form a basis for $col(A)$. What are they?

Then the canonical solutions of Ax=0 form a basis for $null(A)$. These are readily obtained from the system Rx=0, where R is the reduced matrix of A).