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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 1. Decide the orthogonal projections matrix Pw 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). Tags calculating, matrix, projection how to recognize a projection matrix

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