5 Section 2C, 3A and 3B - Dimension, Linear Transformations, Null Spaces and Ranges Problem 1 Write down the denition of dimension of vector space. Problem 2 What is the dimension of P[$]512 = {p E P[3:] : degree p S 12}? Problem 3 Let T : V > W be a function. Write What it means for T to be linear. Problem 4 Let V, W be nite dimensional vector spaces. If T : V > W is linear, injective and surjective Show that the dimension of V is the dimension of W. You may only use results from Section 3B and before