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Consider the vector v = (4, 1, -2) in R3 Let V be the subspace of R3 consisting of all

Linear Algebra with Applications | 8th Edition | ISBN: 9781449679545 | Authors: Gareth Williams ISBN: 9781449679545 435

Solution for problem 5 Chapter 4.7

Linear Algebra with Applications | 8th Edition

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Linear Algebra with Applications | 8th Edition | ISBN: 9781449679545 | Authors: Gareth Williams

Linear Algebra with Applications | 8th Edition

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Problem 5

Consider the vector v = (4, 1, -2) in R3 Let V be the subspace of R3 consisting of all vectors of the form (a, 2a, b). Decompose v into the sum of a vector that lies in V and a vector orthogonal to V.

Step-by-Step Solution:
Step 1 of 3

8.1 Integration by Parts ❑ ❑ ❑ ❑ ❑ Deals with: ∫ xe dx, ∫ xcos(2 x)dx∫, l| | d∫ , e c(x)dx , etc… ❑ ❑ ❑ ❑ Consider: u(x) & v(x) 2❑different❑able functions: (❑*v)’=(u*v’)+(u❑*v) &(integrate ' with respect to x) uv= ∫ uv )dx+∫(u' v)dx ∫ uv' dx=uv- ∫ u' vdx ❑ ❑ ❑ ❑ ❑ ❑ udv=uv− vdu ❑ ∫❑ x x xe dx u=x dv=e dx du=dx v=e x Ex. ❑ *Let dv be the easiest part of the integrand ¿ ∫❑ ❑ ❑ ❑ x x x x❑ x x ∫ xe dx=xe − e∫dx ∫ xe dx=xe −e +C ❑ ❑

Step 2 of 3

Chapter 4.7, Problem 5 is Solved
Step 3 of 3

Textbook: Linear Algebra with Applications
Edition: 8
Author: Gareth Williams
ISBN: 9781449679545

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Consider the vector v = (4, 1, -2) in R3 Let V be the subspace of R3 consisting of all