Prove that if V = M (Direct sum) N, then
V/M (Isomorphisms.) N. Hint: Restrict the quotient mapping V /M to N and the kernel and image of the restricted mapping.
plx help
As any has a unique expression as , define by
Uniqueness of expression gives you that f is well defined, and now just prove that f is an isomorphism of vec. spaces.
Tonio
Pd. Of course, f is NOT an isomorphism! You need to find its kernel and use the fist isomorphism theorem