Unformatted text preview: n × n matrix A is Gaussian equivalent to a triangular matrix. Solution. Absent. 4.27 Prove that Ax = β is consistent if and only if β lies in the column space of A . Solution. If γ ∈ k m , then A γ 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 α 1 , . . . , α n be the columns of an m × n matrix A over a f eld k , and let β ∈ k m . (i) Prove that β ∈ h α 1 , . . . , α n i if and only if the inhomogeneous system Ax = β has a solution. Solution. Absent....
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- Fall '11
- Linear Algebra, Solution., Aγ