Let T: U V be a linear transformation. Prove that dim range(T) = dim domain(T) if and only if Tis one-to-one.

Math 1311 Section 1.1 Functions Given by Formulas Topics: Using function notation Domain Answering questions when given a formula functions Using TI to compute function values and using the “Ans” feature of the calculator What is a function Definition: A function is a rule that assigns to each element of one set (which we call the domain) exactly one element of some other set (which we call the range). Example 1: a. If you are driving across the country, you can write a function that gives the distance you have traveled. If you travel at 65 miles per hour, this could be your function: = × = 65 × b. If you