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January 4th, 2014, 01:03 PM   #1
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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
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January 4th, 2014, 03:07 PM   #2
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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
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January 6th, 2014, 07:48 AM   #3
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Re: calculating projection matrix

I have solved it, was pretty straight forward
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January 7th, 2014, 12:58 PM   #4
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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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