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January 4th, 2014, 01:03 PM  #1 
Newbie Joined: Nov 2013 Posts: 4 Thanks: 0  calculating projection matrix
Let W be the solutionset to: Code: x1  x2 + x3 = 0 x1 + 2x2 + x3 = 0 I know how to calculate the projection matrix the problem is i dont know how to find the basis for the basis W 
January 4th, 2014, 03:07 PM  #2 
Newbie Joined: Nov 2013 Posts: 4 Thanks: 0  Re: calculating projection matrix
meant  'I know how to calculate the projection matrix the problem is i dont know how to find the basis for W' ofcourse

January 6th, 2014, 07:48 AM  #3 
Newbie Joined: Nov 2013 Posts: 4 Thanks: 0  Re: calculating projection matrix
I have solved it, was pretty straight forward

January 7th, 2014, 12:58 PM  #4 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: calculating projection matrix
For those who were wondering, by subtracting the first equation from the second, both x1 and x3 are eliminated leaving 3x2= 0 so that x2= 0. With x2, both equations become x1+ x3= 0 so that x3= x1. That is, any solution the equations is of the form (x1, x2, x3)= (x1, 0, x1)= x1(1, 0, 1). Any solution to that system of equations is a number times the single vector (1, 0, 1) so W is one dimensional vector space with basis the single vector (1, 0, 1).


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