Question attached below. Thanks in advance!

Here is more practice on kernel, range, rank, and nullity. 0 Show that if T : V > W is a linear transformation, then range(T) is a subspace of W. . Consider Maxn. Let S be the subspace of n x n matrices whose elements in the first row sum to zero, and whose elements in the second column sum to zero. Find dim (S). (Hint: Define a linear transformation T : Mnxn - R2 such that S = ker(T) and use Rank-Nullity Theorem). . Consider PAo. Let S be the subspace of polynomials in Po whose coefficients on the even powers all sum to zero. Find dim(S). (Hint: Similar idea to the previous part. )