Precalculus
Name:
Period:
Date:
Chapter 7 Review Test
1. In the following system of equations, solve for X and Y
using substitution (must show work or NO credit):
1.
2.5X + 4Y = 13
X - 4Y = 8
2. In the following system of equations, solve for X and Y
using elimination (must show work or NO credit):
Y = _______
2.
2X + 4Y = 7
-X + 3Y = 4
3. In the following system of equations, solve for X and Y
using any method:
2X - 5Y = 10
3X + 4Y = 9
X = _______
X = _______
Y = _______
3.
X = _______
Y = _______
4. State how many solutions exist for the following systems:
a. 2X + 5Y = 10 and X + 6Y = -5
4a. _______
b. 3Y + X = 2 and .5Y + (X/6) = 1/3
4b. _______
c. 4Y + X = 3 and -10Y + 3X = -9
4c. _______
d. X2 + Y2 = 25 and Y = 2X2 -5X -3
4d. _______
( x) 2 ( y  3) 2
e.

 1 and
16
9
4e. _______
5. Write the order of the following matrices
2 3 6 8 
 4 7 .5 1/ 3


a.
b.
2
5a. _______
0 5
5b. _______
For questions 6 – 9 and 12 use the following matrices:
 3 2 
A

 6 5 
5 1 2 
B

3 4 4
 0 .5 
C

 4 2 
0 1
3

D 4 2
5 

 6 10 4 
6. Perform the following operations (if the operation is not possible
write N/A):
a. A - C
6a. ________________
b. 3A + 1/2C
6b. ________________
c. 1/5(BD)
6c. ________________
d. AB + CB
6d. ________________
7. Verify if B and D are inverses of each other
and state your reasoning
7 Inverses Y or N (Circle one)
Reasons__________________
_________________________
8. Determine the inverse of C without using the calculator
Inverse function (must show work or NO credit):
8 ______________________
9. Determine the inverse of D (round to 2 decimals)
(you may use any method you like)
9 ______________________
10. Solve the following system of equations (you must use matrix
operations) -- (must show work or NO credit):
5X + 3Y = -7
.4X - .6Y = 2/3
Matrix Set up:
Inverse Matrix (round to 4 decimals)
Solution (round to 2 decimals):
X = ________
Y = ________
11. (EC) Solve the following system of equations (method of your choice)
5X -3Y + 2Z = 2
3X + 4Z = 3
-X + 7Y - .8Z = 4
11.
X = ______
Y = ______
Z = ______
12. Determine the determinant for C (see previous pages for C)
leave answer as a fraction
13. (EC) Determine PXQ for the following vectors:
State answer in component form
P = 10i, 0j, 5k
Q = 3i, -2j, 2k
12. ____________
13 ___________________
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Chapter 7 Review