State with a brief explanation whether the following statements are true or false. (a) The vectors (1, 0) and (0, 1) span R 2 .
(b) The vectors (1, 0), (0, 1), and (1, 1) span R 2 .
(c) The vectors (1, 0) and (0, 1) are linearly independent.
(d) The vectors (1, 0), (0, 1) and (1, 1) are linearly independent.
(e) A set of any two vectors in R 2 is a basis for R 2 .
(f) A set of any three vectors in R 2 must be linearly dependent.
(g) R 2 is a subspace of R 3 .