Problem 12. (9 points) Let A = aand Find the dimension of the kernel and the dimension of the image of the linear transformating T(x) = Ax. dim(Ker(A)) = dim(Im(A)) = Are the following statements h ? A combination of Proposition 7.26 and Theorem 7.45. ? V Theorem 7.38. ? VTheorem 7.43. ? V Theorem 7.52. Note: You can earn partial credit on this problem.Proposition -. Vectors 51,621.\Proposition 7.38. (1) For any matrix A, rank A = rank(AT). (2) If A is a m x n matrix, then rank A