Recent content by Lostmant

Got it. Thanks so much.

Thank you jbunniii. Using the hint you gave me I could prove that Kernal (A^n) is a subspace of Kernal (A^(n+1)), because A^n(A(0)) = 0. but what about range? I think if i could prove the range of A is always a subspace of domain of A, then i am done. How to prove this? Thanks.

Homework Statement How to prove that: the range of a square matrix A (linear transformation) to the power of n+1 is a subspace of the Range of A to the power n, for all n >= 1? i.e. Range (A^(n+1)) is a subspace of Range (A^n) Homework Equations The Attempt at a Solution I...