Algorithmic Mathematics

Exercise 6.5. Let F=Q. R, C, or Z/(p), p a prime (or indeed let F be any field), and let v...,04EP (a) Let 04EF. Prove that (01,...,0k-1, QUk) (01,...,UK). (b) Prove that if the sequence (01.0k) is in echelon form, then 01.... Uk are linearly independent. (c) Let F = Z/(P), p a prime. Using Echelonize, prove that if W is the subspace of generated by the vectors W = (W1,...,m), then #W = p', for some s, with 0