Homework #5 N co Suppose A is a matrix and is an eigenvector corresponding to 1 = -5, and is an -3 eigenvector corresponding to 1 = -4. Find the following. - 3 Co 2 -1 A = -3 4 A -3 2 A +Suppose 38 30 A= [42 33} Find the matrix A32 (enter each answer as a mathematical expression and not a number in scientific form) A32 . ) -2 0 0 Find an orthogonal diagonalization for A = [ 0 -2 1} ; 0 -1 -2 i.e. find an orthogonal matrix U and a diagonal matrix D such that A = UDU". Any empty entries are assumed to be 0. d | 100" 00C 100 00C 100 00C A company rents moving trucks out of two locations: Tampa and Pittsburgh. Some of their customers rent a truck in one city and return it in the other city, and the rest of their customers rent and return the truck in the same city. The company owns a total of 500 trucks. The company has seen the following trend: About 45 percent of the trucks in Tampa move to Pittsburgh each week. * About 75 percent of the trucks in Pittsburgh move to Tampa each week. Suppose right now Tampa has 170 trucks. How many trucks will be in each city after 1 week? [Round answers to the nearest whole number.] Tampa: Pittsburgh: How many trucks will be in each city after 4 weeks? [Round answers to the nearest whole number.] Tampa: Pittsburgh: T2 &5 is the number in Pittsburgh, find the matrix A so that At is the distribution of trucks after 1 week. = Iq If the vector t = [ ] represents the distribution of trucks, where z; is the number in Tampa and