Please help

Adobe Reader Touch X ASSIGNMENT 04 Due date: Thursday, 30 April 2020 UNIQUE ASSIGNMENT NUMBER: 897728 ONLY FOR SEMESTER 1 INSTRUCTIONS FOR THE ASSIGNMENT Take care to explain all your arguments. If you choose to submit via my Unisa, note that only PDF files will be accepted. Problem 10. Let V be a finite dimensional vector space and U C V is a subspace of V. Let W be any vector space Show that for every fe C (U, W) there exists a g E C (V, W) such that for each u E U, g(u) = f(u). Is this g unique? [5 marks] Problem 11. Suppose that V is a finite dimensional vector space with dim V 2 2. Prove that there exists f, ge C(V, V) such that fog # gof. [5 marks] then show that: Problem 12. If U, V and W are finite dimensional vector spaces, g E C(V, W) and f e C (U, V) dim null gof EC}. [5 marks] [Total: 20 marks] - End of assignment - 20