Question

Find the orthogonal projection of v onto the subspace w spanned by the vectors ui

Answer 1

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v = [1,2,3] and u1 = [1,1,1,] and u2 = [1,-1,0]

u1.v = 6 u1.u1 = 3 u2.v = -1 u2.u2 = 0

projw(V) = (u1.v/u1.u1)u1 + (u2.v/u2.u2)u2

projw(V) = (6/3)[1,1,1] + (-1/0)[1,-1,0]



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