253Homework8

Linear Algebra with Applications (3rd Edition)

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ma253 ,Fa l l 2007 — Problem Set 8 Bases, dimension, coordinatization, and the matrix of a linear transformation: all neat stuff. This is due on Wednesday, November 14 . 1. Problems from the textbook: a. Section 3 . 3 , problems 43 , 44 , 47 ,* 62 ,* 63 ,* 64 . b. Section 3 . 4 , problems * 2 ,* 4 ,* 8 ,* 14 ,* 18 ,* 20 ,* 24 ,* 30 . c. Section 4 . 2 , problems 63 ,* 70 ,* 72 , 78 ,* 80 . d. Section 4 . 3 , problems 1 ,* 3 ,* 4 ,* 20 ,* 22 ,* 28 ,* 32 . *2. Suppose { ~ v 1 ,..., ~ v k } is a set of vectors that spans a vector space V ,andthat T : V - W is a linear transformation that is onto. Show that the set { T ( ~ v 1 ) ,...,T ( ~ v k ) } spans W . *3. Suppose { ~ v 1 ,..., ~ v k } is a linearly independent set of vectors in a linear space V , and that T : V - W is a linear transformation that is one-to-one. Show that the set { T ( ~ v 1 ) ,...,T ( ~ v k ) } is a linearly independent subset of
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253Homework8 - ma253, Fall 2007 - Problem Set 8 Bases,...

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