Math20lgOct Two options concerning exam grades: You find out your exam grade as 1. soon as possible, but then you'll have to wait however long it takes for them to be physically returned to you. No questions about exams or the grade listed until after you get it physically returned. You have to wait to find out the 2. grade until the exam is physically returned. You will not have to wait long after receiving these before asking questions. Today : Proof of dimension, the four fundamental subspaces and their dimensions, linear transformations
Basis Goldilocks enough vectors to span the space not too many so they are still indep vis gun is a basis for V if it is linearly independent and warning span Vi gun U V us gun Also We will alway write a basis as um un and hot vision on Cu un theorem If us gun and wi own are both bases for V then men Definition The dimension of a vector space V is the number of vectors in a basis for it Call it dim u
proofofthearen us sum wi own are bases for the space V Want n m Suppose n m B c vis gun is a basis we can uniquely write W I A V taz Vat am Vm Sim for all jab oh we can write Wj É Aioli for some Ai EIR I Anjum Wj I Aint Convert these eqs to one matrix eq W win witchu unfit I BA A Airi is
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