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Unformatted text preview: 11 52 56 5. Theorem 11 from section 4.5 of the book tells us that given any linearly independent vectors { v 1 , v 2 ,... v p } in R n , we can extend it to a basis for R n by adding np vectors to it. However, it doesn’t really give us an idea of how to actually do this. Here’s one possible way: create the matrix A = [ v 1 v 2 ··· v p e 1 ··· e n ] ( e i are the columns of the identity matrix) and then use methods we already know to ﬁnd a basis for Col A. (a) How do you know the basis you come up with will be a basis for R n ? (b) How do you know it will include the vectors v 1 , v 2 ,... v p ? (c) Use this method to extend the following set of vectors to be a basis for R 4 : v 1 = 1 2 1 , v 2 = 3 82 3...
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This note was uploaded on 11/19/2010 for the course LECTURE 1 taught by Professor Yildiz during the Fall '10 term at Berkeley.
 Fall '10
 yildiz
 Math

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