True or False:

f.) If T is a linear transformation, then T(u+v)=u+v for all vectors u and v.

g.) If A is any square matrix, then the matrix B = A + AT is symmetric.

h.) If A is a square matrix such that Ax = b has a solution for some particular vector b, then A is invertible.

i.) Every matrix A has an LDU factorization.

j.) Let A be an mn matrix, and B an nr matrix. Then the null space of B is a subspace of the null space of AB.