Let S be a maximal linearly independent subset of a vector space V. That is, S has the property that if a vector not in S is adjoined to S, then the new set will no longer be linearly independent. Prove that S must be a basis for V . [Hint: What if S were linearly independent but not a basis of V?

Thinking Critically with Psychology Science Why do Psychology How can we differentiate between uninformed opinions and examined conclusions The science of psychology helps make these examined conclusions, which leads to our understanding of how people f eel, think and act as they do! What about Intuition and Comm on Sense Many people believe that intuition and common sense are enough to bring forth answers regarding human nature. Intuition and common sense may aid queries, but they are not free of error (What is common sense to us may not be common sense to everybody else) Hindsig