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(Solved): 5. (3 Points) Suppose V Is A Subspace Of R”. A. Suppose X E V And X + Ay V. First Show Ay E V, The...


5. (3 points) Suppose V is a subspace of R”. a. Suppose x e V and x + ay V. First show ay E V, then show if in addition, a +

5. (3 points) Suppose V is a subspace of R”. a. Suppose x e V and x + ay V. First show ay E V, then show if in addition, a + 0, then y EV. b. Suppose x E V and y ER". Use part (a) to show that if r > 0) and B,(x) CV, then y EV. c. Use part (b) to show that if V has an interior point, then V = R”.


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