Find a basis for the subspace S in R4 spanned by all solutions of x1 + 2x2 + 3x3 X4 = 0. Find a basis for the orthogonal complement of S. Find b₁ in S and b2 in the orthogonal complement of S so that b₁ + b₂ = b = (1, 1, 2, 4).

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