Exercise 1 (5 points each). For each of the following statements, determine if it is true or false. If true1 provide a proof. If false, give a counter-example {and show that it is indeed a counter- example). {a} if V is a 1vector space other than the zero vector space, than V contains a subspace W such that W 9'5 V. (b) Nonzero I, y E R3 are linearly,r dependent if and only if 1' H y (this is notation for parallel: there exists a t E R such that :1: = ty). (c) Nonzero 13y. z E R3 are linearlg.r dependent if and only if two of the three vectors are parallel (that is, either I H y, 1' || 3, or y H 2;]. (d) if my, z E V are linearly independent, then they form a basis for span{:r,y,z}. Here, V is a vector space; do not assume that V satises any special properties aside from the vector space axioms. (e) If :r, y, z E V are linearlyr dependent, then .1: + y, 2y, y + z are linearly dep-dent as well. Here. V is a vector space; do not assume that V satises any special properties aside from the vector space axioms