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10 Nov 2019
Let V be a n-dimensional vector space over a field F with basis alpha = {v1, v2, Â ,vn} and let u1, u2, Â , uk be vectors in V. Prove {u1, u2, Â uk} is linearly independent n V iff ([u1] alpha, [u2] alpha, Â .. [uk] alpha) is linearly independent in F .
Let V be a n-dimensional vector space over a field F with basis alpha = {v1, v2, Â ,vn} and let u1, u2, Â , uk be vectors in V. Prove {u1, u2, Â uk} is linearly independent n V iff ([u1] alpha, [u2] alpha, Â .. [uk] alpha) is linearly independent in F .