Abstract algebra

2. Consider the following matrices. a) Let A = [31. i]: a matrix over C, where i = V 1 E 0:. Find a unitary matrix U such that U*AU is a diagonal matrix, where U* denotes the conjugate transpose. b) Let B = i '31] a matrix over C. Find a matrix T such that J = T'IBT is the Jordan normal form of B. c) For the matrix B above, compute exp(B). d) Let C = [i g g E] a matrix over |F-,. What is (dim ColC + dim Null C)? Explain your answer or Show your working. (Here, ColC stands for the column space, and NullC stands for the nullspace.)