Let L : Rn --> Rm and M : Rm --> Rp be linear mappings.
a)Prove that rank( M o L) <= rank(L).
b)Give an example such that the rank(M o L) < rank(M) and rank(L)
The Attempt at a Solution
a)I see that (M o L) takes all vectors in Rn and maps them to vectors in Rm then maps these vectors to vectors in Rp. (L) also takes all vectors in Rn and maps them to Rm. From this, i get the impression that rank(M o L) = rank (L) because the quantity of vectors should not change when (M o L) maps vectors in Rm to Rp.
b)Is there a method to get such a matrix or do I have to use trial and error?