Question 2 Column sums Let M be an m X a matrix with real entries. Assume that the entries in each column of M add up to zero. o (a) Show that the linear transformation T: IR\" ) Rm, :1: I> M 3'? is not surjective. Hint: You might like to play armmd with some small examples, e.g. for m = 2 or m = 3. (1)) Find a non-zero vector in the null space of the transpose matrix W. Justify your answer. (c) Assume now that m = n. Show that the null space of M is non-trivial, i.e, contains a non-zero vector