1!:thst (30 poitS) Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the Textbook. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the Textbook. a) The set of all rst-degree polynomials with the standard operations is a vector space. b) A set S = {12, ,1;2 ,. . . ,vk} , k 2 2 is linearly independent if and only if at least one of the vectors vi can be written as a linear combination of other vectors in S. c) lfA is an m x n matrix of rank r , then the dimension ofthe solution space of Ax = 0 is m - r. W (40 points) Determine whether the given subset is a subspace of R]. W ={(xl,x2,x3): 3c1+362+.t:3 =1}