MATH307 April 2013
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Question 04 (a)
Let S be the subspace of spanned by , and . Given the MATLAB/Octave calculation
> rref([1 2 4; 1 -1 1; 1 -1 -1])
1 0 2
0 1 1
0 0 0
(a) Find the matrix P that projects onto S.
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We are given and its reduced row echelon form
If we take the original matrix as A, then is not invertible, so we cannot obtain P. So, we need to find another matrix.
Since column 1 and column 2 are pivot columns, we take corresponding columns of A.
Those are and , and they are linearly independent.
So, we define a new matrix
Projection matrix is given by
So, if we substitute and , we get