The vectors u1 = (1, 1, 1, 1), u2 = (0, 1, 1, 1), u3 = (0, 0, 1, 1), and u4 = (0, 0, 0, 1) form a basis for F4. Find the unique representation of an arbitrary vector (a1, a2, a3, a4) in F4 as a linear combination of u1, u2, u3, and u4.
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