Question: 6. Let a, b and c denote three elements in a vector space E over the field of complex numbers. Define u = b+c,

6. Let a, b and c denote three elements in a vector space E over the field of complex numbers. Define u = b+c, v=c+a, w= a+b 1) Show that the vector subspaces generated by a, b, and c on the one hand and u, v, and w on the other are identical 2) Show that the vectors u, v, and w are independent if and only if a, b, and c are independent.

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