Name:_ Linear Algebra; Practice Exam 2; Spring, 2008 Show all your work if you want partial credit. 1. Given that
A
2 2
1 3 4 ,B 4 1 0
1 5 2 6 . 3 7 4 8
Compute (if possible) each of the following: (a) AB (b) BA (c) BTA (d) (AB)T (e) A - BT (f)
Name:_ Linear Algebra Practice Exam 1 Spring, 2008 Show all your work on the pages of this exam. 1. Let
1 0 0 2 A 0 1 0 3 0 0 1 4 1 0 0 1 ,B 1 0 0 2 3 0 1 0 3 4 0 0 1 4 3 1 0 0 1 2 ,b 3 4 3 2 ,x x1 x2 x3 x4
(a) To zero out the 1 below the diagonal i
Name:_ Linear Algebra Practice Exam 3 Spring, 2008 1. Let A = PDP-1 and compute A4, where
P
2 -3 ,D -3 5
1 0 . 0 1/2
2. Let the matrix A be
5 0 6 2 1 7 3 0 . 2
(i) Find the characteristic equation of A. (ii) Solve the characteristic equation of