The discussion revolves around the properties of an invertible 3x3 matrix, specifically focusing on the concept of its nullspace and how it relates to the matrix's column vectors.
There is an ongoing exploration of the definitions and properties related to invertible matrices and their nullspaces. Some participants have provided clarifications regarding the nature of the nullspace, while others are questioning their understanding of the concepts involved.
Participants are navigating the distinction between nullspace and column space, with some confusion noted regarding the definitions and implications of invertibility.
charlies1902 said:Let's say you have a 3x3 matrix and it's invertible. Let's call it A
If you were to find a basis for the nullspace of A, would the basis just be the original 3 column vectors of A?
charlies1902 said:It would be the column vectors of A right?
Dick said:Ok, so you don't know what "invertible" means. Could you maybe look it up?
charlies1902 said:det≠0 and a pivot is in every column for RREF(A).
So for a 3x3 invertible matrix,it's basis is [1 0 0]^t [0 1 0]^t and [0 0 1]^t?
Dick said:That's an example of an invertible matrix. What vectors are in its null space?
charlies1902 said:The 0 vector?
Dick said:Yes. Wouldn't that always be the only answer if A were invertible?
charlies1902 said:I think I got it confused with the column space.
A basis for the column space for this case would be the original 3 column vectors if A right?