Problem 4. (3.4/71) Suppose the matrix A is similar to B, with B = SHAS a. Show that if x is in ker(B), then Sx is in ker(A). b. Show that nullity(A) = nullity(B). Hint: If {V,, v2,..., v} is a basis for ker(B), then the vectors (Sv1, SV2,..., Sv } in ker(A) are linearly independent. Now reverse the roles of A and B