Recent content by JKCB

Ah! Well that's going to be fun! Thank you so much!

What do I do with the 2 at the end of the original equation?

Homework Statement Homework EquationsThe Attempt at a Solution 4x^2-2xy=2-3y^2 x(4x-2y)=2-3y^2 then I'm stuck[/B]

Yes I am talking about the linear transformation, sorry. For some reason, its hard for me to let the nullity be that large. Most of the problems I have worked had a nullity of 0 or 1. This one threw me a little(lot). Thank you. Your detailed explanation is wonderful. Sorry to be so dense.

Thank you all, I'm feeling quite not so smart! HallsofIvy that makes sense, so if I had just said the sum of the diagonal must equal zero and not used the notation that I used that would have been correct? Which means the nullity of the trace is equal to 1?

Homework Statement What is the nullity of the trace (A), A is an element of all nxn square matrices. The Attempt at a Solution the null space would be when the sum of the diagonal is equal to 0. So the Σaii for i=1 to n must equal 0 which would be when aii = -aii. Therefore the...

No. How about this? A= (Im 0)P where P is an nxm invertible matrix. Then replace A with (Im 0)P(B) = I am then (Im 0) P P^-1(Im)=Im (0 ) (that is a column block matrix with I am being the Identity matrix and 0 being a zero matrix...

Im (I subscript m) is the mxm identity matrix and 0 is the m x (n-m) zero matrix.

Yes I am is the mxm identity matrix and 0 is the mxn zero matrix. I'm thinking of going another direction. What if I start with letting B be any nxm matrix with rank n. Then AB would be an mxm matrix with rank m, then by the Thm (in my book) 2.18 corollary 2 an nxn matrix is invertible...

Homework Statement Let A be an m x n matrix with rank m. Prove that there exists an n x m matrix B such that AB=Im The Attempt at a Solution I'm assuming I would need to start with the def. That there exists P an mxm invertible matrix and Q an nxn invertible matrix s.t. A=P(Im 0)Q...