1. label the following statements as true or false. a. an injective linear map t : u ? v maps linear independent vectors to linearly independent vectors. b. any set of linearly independent vectors vi, v2, ,vk n rn can be extended to a basis by adding n- kunit vectors c. any subspace of r" is the solution-space of a linear system ax-0. d. elementary row operations on an m x n-matrix a don't change the space generated by the columns of a e. elementary row operations on an m x n-matrix a don't change the space generated by the rows of a f. a linear system ax- 0 of m -equations in n-unknowns has always a nontrivial solution ifnnm g. if an m x n-matrix a has r-many linearly independent rows than it also must have n many linearly independent columns h. the determinant function det is a linear function on the vector space of n x n-matrices l. let a be an n × n-matrix. then det(cd) c det(a). j. for any n x n-matrix a one has that det(a"(a) (a" 1s the transpose ofa.)