Question: Suppose that the linear system allx1 + a12x2 + . . . + aintn = C1 a21 X1 + a22x2 + . . . +

Suppose that the linear system allx1 + a12x2 + . . . + aintn = C1 a21 X1 + a22x2 + . . . + a2nan = C2 . . . akix1 + ak2x2 + . . . + aknan Ck has a solution Xi = (X1, . . ., In ) for each Ci = (C1, C2, . .., Ck ) in {c1, . .., Cn }. Prove that the linear system has a solution x for each c in Span(c1, . . ., Cn)

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