(Solution) - a Show that if v is a linear combination of -(2025 Original AI-Free Solution)

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(a) Show that if v is a linear combination of v1.......vm, and each vj is a linear combination of w1,..., wm then v is a linear combination of w1..........wn.
(b) Suppose v1.....vm, span V. Let w1,..., wn ? V be any other elements. Suppose that each vi can be written as a linear combination of w1.............. Prove that w1.......wn also span V.