True or False:

a.) If a linear system has infinitely many solutions, then there are more variables than equations.

b.) Every homogeneous linear system has at least one solution.

c.) If u, v,and w are vectors,then u(v +w)=(uv)+(uw).

d.) If the columns of a matrix A with n rows and m columns do not span Rn, then there exists a vector b in Rn such that Ax=B does not have a solution.

e.) If {u1 ,u2}, {u1 ,u3}, and {u2 ,u3} are all linearly independent, then {u1, u2, u3} is linearly independent.