Math 140. Test 3 (v2) (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 M21,M22 and M23? What are the cofactors A21,A22,A23 ? What is the
determinant of M?
2. (10 points) Perform the matrix multiplication:
1 2 x
2 1 4
3 0 3
·
2 1 y
1 2 −1
3 4 0
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:
2 1
3x+ 2 3y
−1 1=z4
1 2
5. (10 points) We want to make 20 gallons of a 16% 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:
(3x+y= 5
4x+y= 2
7. (8 points) Which of the following matrices are in row echelon form?
A=
2 1 4 0
0 4 3 0
0 0 1 0
B=
1 0 0 0
0 1 5 9
0 0 1 7
C=
1 0 1 1
0 1 0 0
0 0 0 0
D=
1 0 0 4
0 1 0 5
1 0 1 8
