Math Is Fun Forum

Identity

Member

Registered: 2007-04-18

Posts: 934

Finding the null space of a matrix equation

(Ugh I meant nullspace, don't know why I said solution space!)

I was watching an MIT OCW lecture on linear algebra and the guy wanted to find the null space of

After getting it to reduced row echelon form,

The lecturer asks us the 'notice' the identity matrix in the pivot columns, then he writes down:

And since that is in the form

, the solution space must be

so that

So the solution is:

But there are a few things I don't understand about it... to get it into the form of matrix R, you have to swap two columns. Is this allowed?

Also, isn't

a 4x2 matrix? Then how come the solution is written as a linear combination of vectors?

Last edited by Identity (2009-11-17 14:50:44)