Mat 313: elements of linear algebra (page 1 of 2) (1) (20 points) let a be an nx n matrix. determine which (if any) of the statements are equivalent to the statement the matriz a is invertible. (a) the columns of a are linearly independent. (b) the columns of a span rn. (c) the null space of a is trivial, e. nul(a)-0) (d) there is only one solution to the equation ax = 0 and it is the x = 0. (e) the unique linear map ta : r" r, defined by a, is one-to-one. (f) the unique linear map ta : r"r, defined by a, is onto. (g) the rank of a is n. (h) det a 0.