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Question: Determining Elements of the Span of a Set of Vectors

Question:Determining Elements of the Span of a Set of Vectors

DJJerome1976 540 Maple
linear-algebra
October 22 2023
1

Suppose I have a set of vectors, say S = {x+4, 3x-7}, a specific vector f = -5x + 10 and I would like to determine if f is an element of Span(S). By hand it's a rather simple process, check the consistency of the corresponding linear system. Is there a way to automate this in Maple? That is, define a vector space (using any finite vectors: polynomials, matrices, etc.) with some basis and check to see if a given element belongs to that space? Moreover, if it does belong, could we get the linear combination of the elements of the basis that produces the desired vector?
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