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Unformatted text preview: n n matrix A is Gaussian equivalent to a triangular matrix. Solution. Absent. 4.27 Prove that Ax = is consistent if and only if lies in the column space of A . Solution. If k m , then A is a linear combination of the columns of A . 4.28 If A is an n n nonsingular matrix, prove that any system Ax = b has a unique solution, namely, x = A 1 b . Solution. Absent. 4.29 Let 1 , . . . , n be the columns of an m n matrix A over a f eld k , and let k m . (i) Prove that h 1 , . . . , n i if and only if the inhomogeneous system Ax = has a solution. Solution. Absent....
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- Fall '11