1. The problem statement, all variables and given/known data Let A be n x n, λ ∈ ℂ, let v be n x 1, and suppose that A ⋅ v = λ ⋅ v. Show that A^j ⋅ v = ^j ⋅ v for each positive integer j. 2. Relevant equations 3. The attempt at a solution I haven't been able to get very far but, ^j ⋅ v - A^j ⋅ v = 0n x 1 v( ^j - A^j) = 0n x 1 Not sure how to prove that for every positive j that this is true. Any thought would be appreciated. Thanks.