I have a test soon I'll apprieciate if you'll help me:

1. let V be vector space. and let T:V-V be a linear transformation that sustains dimImT=1 and .

prove that T has an eigenvalue that is different from zero.

let n=3. prove that V has a basis B and there is a scalar such as

2. given unhomogane set of linear equations in 4 veriables, that the vectors

are solutions to it. find the general solution of the system!!

3. let A,b be nxn matrixes. given that (I-A) and (I+B) are similar prove that are also similar!!!

Thanks ahead (srry about the bad english)