Recent content by dyanmcc

dimension of kernel equal 2. Dimension of range equals 2. dimension of domain equals 4. Since dim range = 2 and F^2 is the whole space of the range, then it is surjective?

the dimension of the kernel is two, the dimension of the range is two so F^2 equals dim range and therefore is surjective?

I'm having trouble with this: Prove that if P is a linear map from V to V and satisfies P^2 = P, then trace P is a nonnegative integer. I know if I find the eignevalues , their sum equals trace P. But how do I find them here? any thoughts? Thanks

In my head this proof seems obvious, but I am unable to write it rigorously. :cry: Any help would be appreciated! Prove that it T is a linear map from F^4 to F^2 such that kernel T ={(x1, x2, x3, x4) belonging to F^4 | x1 = 5x2 and x3 = 7x4}, then T is surjective.

Great thanks. Here's another one for you...Prove that if V is finite dimensional with dim V > 1, then the set of noninvertible operators on V is not a subspace of L(V)

Hi, I don't know how to do the following proof: If (v1, ...vn) are linearly independent in V, then so is the list (v1-v2, v2-v3, ...vn-1 -vn, vn). I can do the proof if I replace 'linearly independent' with 'spans V' ...so what connection am I missing? Thanks much!