MAT 208 Instructor: Mike Wang
NAME:
Sample Midterm
Show all your work clearly! If you nish early, dont forget to check your work.
1. Answer the following: (20 pts) (2 pts each)
* (True or False): If A is an (m x n) matrix and B is an (n x p) matrix, then
Math 208, Final Exam
(1) Let A =
1 3
4 2
,
b=
1
2
. Find the following:
(a) At + I
(b) detA
(c) A1
(d) The eigenvalues of A.
(e) Using Gauss-Jordan elimination solve Ax = b.
x1 + x2
0
(2) Let L : I 3 I 2 where L(x) =
R
R
(3 points each)
.
(a) Prove that L
Math 208, Exam 1
Let
1 2 1
A= 1 3 4
0 2 1
1 1 2
B= 3 1 0
2 0 3
4
C= 1
7
Problems 1 thru 6 use the matrices above:
(1) 3A + B
(5pts)
(2) AC
(5pts)
(3) C T B
(5pts)
(4) B 1
(10pts)
(5) Bx = C (free to choose, though one is quick)
(10pts)
(6) Write A as a
Midterm for Mat 208
(1) Let
1 2
A = 5 4
6 0
B=
5 3 6
0 2 5
Calculate the following:
(a) A + 2B t
(b) BA
(c) Solve A = C, what is your conclusion?
x
(2) Find A, given that
(3A)1 =
4 1
2 3
1
C= 4
6
(3) A matrix A is said to be orthogonal if A1
1 2 1
= At