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)