Question: Problem 8. Let V and W be vector spaces over IF. Let V X W = {(1), w) : 'U E V, w E W}.

Problem 8. Let V and W be vector spaces over IF. Let V X W = {(1), w) : 'U E V, w E W}. Show that V X W is a vector space under the operations (01,101) + (v2,w2) ('01 + 13,101 + 1122) and afvgw) 2 (at), am) for a 6 IF. The vector space V X W is known as the direct product of V and W

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