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If b l c, :: :: I = - 2. find ('2 c ) {I I - ~(/ ) a, a, iJl - ~b) b, b, , C l - 1:c) c

Elementary Linear Algebra with Applications | 9th Edition | ISBN: 9780132296540 | Authors: Bernard Kolman David Hill ISBN: 9780132296540 301

Solution for problem 4 Chapter 3.2

Elementary Linear Algebra with Applications | 9th Edition

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Elementary Linear Algebra with Applications | 9th Edition | ISBN: 9780132296540 | Authors: Bernard Kolman David Hill

Elementary Linear Algebra with Applications | 9th Edition

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Problem 4

If b l c, :: :: I = - 2. find ('2 c ) {I I - ~(/ ) a, a, iJl - ~b) b, b, , C l - 1:c) c, ' )

Step-by-Step Solution:
Step 1 of 3

1 MATH 205 LINEAR ALGEBRA SUPPLEMENT STEVEN H. WEINTRAUB 1. Coordinates and Change of Basis Definition 1.1. Let B = {v ,v1,..2,v } bn a basis for the vector space V . Let v ∈ V so that v = c 1 1 c 2 +2▯▯▯ + c vn n for unique scalars 1 ,2 ,...,n . The scalars 1 2c ,...nc are called the coordinates of v in the basis B, and the vector   c1  c2 [v]B=  . . c n is called the coordinate vector of v in the basis B. n Definition 1.2. The standard basis for R is E =n{e ,e1,.2.,e } wnere e is ihe vector in R with i th entry equal to 1 and all other entries equal to 0. (We will generally abbreviate E no E when there is no possibility of confusion.)       1 0 0 For example, the standard basis for R is E = {  0 , 1 ,0 }. 0 0 1 Lemma 1.3. Let B = {v ,v 1...2v } benany basis of V . (a) [0B = 0. (b) [v ] = e . i B i Proof. Part (a) is just the observation that 0 = 01 + 0v 2 ▯▯▯ + 0v n Part (b) is just the obser

Step 2 of 3

Chapter 3.2, Problem 4 is Solved
Step 3 of 3

Textbook: Elementary Linear Algebra with Applications
Edition: 9
Author: Bernard Kolman David Hill
ISBN: 9780132296540

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If b l c, :: :: I = - 2. find ('2 c ) {I I - ~(/ ) a, a, iJl - ~b) b, b, , C l - 1:c) c