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1. Let V be a vector space. (a) (12 points) Suppose {v1, .... vx} Spans V. Show that if {v1, ..., x} is linearly de- pendent, you can remove a vector v, such that the remaining set still spans V. (b) (12 points) Suppose {v1, ..., vx} is linearly independent. Show that if {v1, ..., Uk} does not span V, then there is a vector vk+1 E V such that {v1, ..., Uk, Vx+1} is linearly independent