Let b and S be vectors in R*. 2 3 - 7 a) Find projs b...

 

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Let b and S be vectors in R*. 2 3 - 7 a) Find projs b , the projection of b onto the subspace spanned by S = where b .3 2 3 HINT: Are the vectors in S orthogonal? Orthonormal? b) Find the distance from b to W= span(S). 1 3 -1 c) Let A = - 3 1 and b : - 7 Find the least squares solution i to the system Ax = b. 1 -1 3 d) Now compute Ax and Ax – projs b. What do you notice? Let b and S be vectors in R*. 2 3 - 7 a) Find projs b , the projection of b onto the subspace spanned by S = where b .3 2 3 HINT: Are the vectors in S orthogonal? Orthonormal? b) Find the distance from b to W= span(S). 1 3 -1 c) Let A = - 3 1 and b : - 7 Find the least squares solution i to the system Ax = b. 1 -1 3 d) Now compute Ax and Ax – projs b. What do you notice?