This homework is about vectors and matrices. It has a total of 70 available marks. There are no exam style "long answer" questions in this homework. 1. Calculate the dot product u . v in each case: (a) (5 marks) u = v = 3 2 (b) (5 marks) u = -1/3 3/2 U = 2. Calculate Av in each case: (a) (5 marks) A = v = (13) (b) (5 marks) A = 1 1/3) 1 = (3/ 4 3. Calculate both AB and BA in each case: (a) (5 marks) 1/2 (2/3 1/3 B= 1/2 1) (b) (5 marks) A = 14 B = (1/2 -1/2 4. (10 marks) Calculate the determinants and inverses (if they exist) of the following four matrices A = 12 3) B = 3 -1/3 C= (1 " 2 ) D = (21/4 3 4 -11/2)