Math 140. Test 3 (v1) (Fall 2005. Harvey).
Name (2 points):
No notes or texts allowed. You may use a TI-83, TI-84, TI-86 or equivalent calculator. Show all
work.
1. (10 points)
121
211
324
What are the minors M31,M32 and M33? What are the cofactors A31,A32,A33 ? What is the
determinant of M?
2. (10 points) Perform the matrix multiplication:
1 2 3
2 1 4
3 0 x
·
2 1 0
1 2 −1
3 4 y
3. (10 points)
A=
1 0 0
0 2 0
1 4 1
Compute A−1. Show your work (no calculator).
4. (10 points) Find x,y, and z:
2x
3 1+ 2 3 1
−1y=8 4
z2
5. (10 points) We want to make 15 gallons of a 12% salt-water solution. We have a 10% solution
and a 20% solution. How much should we use of each? Set up the system of equations. You may
use your calculator to solve the system.
6. (10 points) Solve the system of equations:
(x+y= 15
2x−y=−3
7. (8 points) Which of the following matrices are in row echelon form?
A=
1 2 4 0
0 1 3 0
0 0 0 0
B=
1 0 0 0
0 2 5 9
0 0 4 7
C=
1 0 1 1
0 1 0 0
1 0 1 0
D=
1 0 0 4
0 1 0 5
0 0 1 8
