Transcription of A GUIDE TO PROOFS IN LINEAR ALGEBRA
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A GUIDE TO PROOFS IN LINEAR ALGEBRA
A GUIDE TO PROOFS IN LINEAR ALGEBRAby Curtis Paul WHAT IS A PROOF? What is a proof and why do we care? Previously in your mathematical life you have mostly focused on computation. You were not concerned with whether or not things were true but with whether you got the right answer. It is not uncommon for students to say, I know the answer. Why do I need to understand the steps? There are a number of responses to this. How do you know your answer is correct? How can you convince someone else your answer is correct? If you are given a harder problem to which you don t know the answer, how are you going to approach it? Proof addresses these concerns. A proof is a sequence of statements justified by axioms, theorems, definitions, and logical deductions, which lead to a conclusion. Your first introduction to proof was probably in geometry, where PROOFS were done in two column form.
We’ll look at some symbolic logic now. Let’s start with the following symbols: P ⇒ Q. Here P stands for a given statement, ⇒ means “implies”, and Q stands for a conclusion statement. ...
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