Thread: 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!

First you have to reduce your matrix to row echelon form. The nonzero rows of this reduced matrix form a basis for . 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 . What are they?

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