253Homework7

Linear Algebra with Applications (3rd Edition)

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ma253 ,Fa l l 2007 — Problem Set 7 Most of this assignment deals with bases and dimension, both in R n and in more general vector spaces. Linear transformations also come in, and the rank and nullity theorem will play role. This is due on Wednesday, November 7 . 1. Problems from the textbook: a. Section 3 . 3 , problems * 18 ,* 22 ,* 26 ,* 28 ,* 30 ,* 36 ,* 38 . b. Section 4 . 1 , problems * 18 ,* 26 . c. Section 4 . 2 , problems * 22 ,* 24 , 25 ,* 27 ,* 32 , 33 ,* 34 ,* 42 ,* 50 ,* 54 , * 60 . *2. In problem 34 from section 4 . 2 , you are asked to work in the space V of all in±nite sequences of real numbers and to consider what is usually called the right shift operator , de±ned by R ( x 0 ,x 1 ,x 2 ,x 3 ,... )=( 0, x 0 ,x 1 ,x 2 ,x 3 ,... ) . Show that ker ( R )= { ~ 0 } ,where ~ 0 means the zero vector in V , i.e., the se- quence ( 0,0,0,0,. .. ) .Is
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253Homework7 - ma253, Fall 2007 - Problem Set 7 Most of...

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