1. Suppose that v?, v? are linearly independent vectors in a vector space V and that v ? V is not contained in span{v?, v?}. Prove that v, v?, v? are linearly independent. 2. Let v? = [2, -1, 1], v? = [1, 1, -1]. If possible, extend the set {v?, v?} to a basis of R3. 3. Let A be an m x n matrix and P an invertible n x n matrix. Prove col(A) = col(AP).
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