Please answer all clearly and legibly. Thank you!

Consider the set V of all ordered pairs of real numbers (x, y) and define the operations @ and @ by (x, y) @ (x', y') = (x+x', y+y') and c o (x, y) = (x, cy). Explain why V is not a vector space? N Which of the following subsets of R are subspaces of R3? The set of all vectors of the form a. (a,b,c) where a = 1 (a,b,c) where a = () c. (a,b.c) where c - b + 3a = 0) Which of the following subsets of Rare subspaces of R ? The set of all vectors of the form a. (a,b,c,d) where a = 2 + b (a,b,c,d) where c = b? c. (a,b,c,d) where a + b = 0 and a + c =d Which of the following sets of vectors are bases for R?? If not, explain why. a. {(1,2). (- 1,1) ; { (1,3), (2. - 3). (0, 2) } (1,2). (2,-3). (3,2); { (2. 4). (-1, 2 ). }