Find the closest point to y in the subspace w spanned by bold v 1v1 and bold v 2v2. yequals=left bracket start 4 by 1 matrix 1st
row 1st column negative 15 2nd row 1st column negative 1 3rd row 1st column 1 4st row 1st column 2 endmatrix right bracket −15 −1 1 2 , bold v 1v1equals=left bracket start 4 by 1 matrix 1st row 1st column 1 2nd row 1st column 1 3rd row 1st column negative 1 4st row 1st column negative 2 endmatrix right bracket 1 1 −1 −2 , bold v 2v2equals=left bracket start 4 by 1 matrix 1st row 1st column 5 2nd row 1st column 1 3rd row 1st column 0 4st row 1st column 3 endmatrix right bracket
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We will have the following:
So, the solution would be: