1 Find the determinant of the matrices 1 3 A= 2 1 4 B= 2 0 −1 − 3 0 7 A group took a trip on a bus, at $3 per child and $3.20 per adult for a total of $118.40 They took the train back at $3.50 per child and $3.60 per adult for a total of $135.20 How many children and how many adults? Find the characteristic polynomial and the real eigenvalues of the matrix a b c d Find the (3,2)-cofactor of the matrix 2 −1 a −2 ; b 3 − , find matrix P so that P −1 AP is diagonal 5 Let A = Find a formula for xk if x0 = 0; x1 = 1; xk + = 10 xk − 3xk +1 Solve the following linear recurrences: xk + = xk − xk +1 ; x0 = 1; x1 =