Null space and column space basis

What I want to share in this blog is a basis of null space and column space.

 

1. a null space and a column space: I told you these in an earlier blog, but I'm going to talk about these again for a quick review. the null space is a set that contains vectors that make an equation a matrix A times a vector x 0. Here it is. 

column space is a lot easier to understand, which is a set of column vectors in matrix A.

** Note that if the null space of A only contains the 0 vector, then these vectors are linearly independent.

2. A basis: the basis is a set of vectors that span a subspace, and they are also linearly independent. In order to make a column space linearly independent, then you have to remove all the free variables in the vector set.