Let T: U V be a linear transformation. Prove that dim range(T) = dim domain(T) if and only if Tis one-to-one.
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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
Textbook: Linear Algebra with Applications
Author: Gareth Williams
Linear Algebra with Applications was written by and is associated to the ISBN: 9781449679545. This textbook survival guide was created for the textbook: Linear Algebra with Applications, edition: 8. Since the solution to 6 from 4.9 chapter was answered, more than 224 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 6 from chapter: 4.9 was answered by , our top Math solution expert on 03/15/18, 05:22PM. This full solution covers the following key subjects: . This expansive textbook survival guide covers 56 chapters, and 1286 solutions. The answer to “Let T: U V be a linear transformation. Prove that dim range(T) = dim domain(T) if and only if Tis one-to-one.” is broken down into a number of easy to follow steps, and 21 words.