Solution

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Again, we set up the equations just as above, but now we get 4 eqautions in 3 variables. So, we go thru the least squares formulation. The problem, then is just like the problem 12 and we get

, and are wanting to solve AX=B

which means we want to calculate the projection of the vector B on the subspace spanned by the columns of A.

The matrix = and its inverse is

The solution is

which we can calculate is without explicitly calculating the projection matrix