Key to In Class Exam 1 Review, Math 166
1. 6 chairs, 1 table, 3 cabinets
2. 1.2 oz of chicken, 2.4 oz of soy, 2.4 oz of rice
3. ( -6 + 3z, 12 – 4z, z) z is any real number, for the context z is between 2 and 3 inclusive. Some particular solutions: no chicken, 4 oz of soy, 2 oz of rice
3 oz of chicken, no soy, 3 oz of rice
1.5 oz of chicken, 2 oz of soy, 2.5 oz of rice
4. r=-8, s=3, t=5/2
5. Addition can only be performed if the matrices have exactly the same size.
Multiplication AB can only be done if A is mxn and B is nxk , the number of columns of A equals the number of rows of B.
If A is mxn, Atranspose is nxm.
If A has an inverse then A is square and nonsingular.
6. Multiply a row by a column with the row on the left.
7. a) 
or 
b) 
or 
8. The necessary row ops are 1/2R3, R2-3R3, R1+5R3.
9. x=1, y= -2-a, z=1+a
11. a) 32.8057554 million units of ag products , 35.03507122 million units of manuf. products and 39.82014388 million units of energy
b) 17.8057544 million units of ag. products, 25.03507122 million units of manuf. products and 31.82014388 million units of energy.
12. a) I will not study or do the review and I will not pass the test.
b)
|
p |
q |
r |
p^q |
~r |
(p^q)v~r |
|
T |
T |
T |
T |
F |
T |
|
T |
T |
F |
T |
T |
T |
|
T |
F |
T |
F |
F |
F |
|
T |
F |
F |
F |
T |
T |
|
F |
T |
T |
F |
F |
F |
|
F |
T |
F |
F |
T |
T |
|
F |
F |
T |
F |
F |
F |
|
F |
F |
F |
F |
T |
T |
|
|
|||||
|
|
|||||
13. a) T b) F
14. a) All those who went over the speed limit or had a traffic accident but who did not receive a ticket.
b) All those who went over the speed limit and did not have an accident or who had an accident and got a ticket.
c) Use DeMorgan’s Law to see how to shade it. This is all those who did not do all three. They did not go over the speed limit, or did not have an accident or did not get a ticket.
15. If you label your letters as done in class with g in the center, then a=6, b=4, c=8, d=9, e=1, f=3, g=5, and h=10.