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Pre Calculus
8.1 - 8.3 Quiz Review
Name _________________________
Date ___________________
Evaluate and simplify the following operations
 4
A
 9
1.
B+D
3.
BAC
5.
CB
2
5 
6. Solve for matrix X:
 3
B
 4
2
6
 5
3 
 1 2
C   3 1 
 3  5
2.
CA
4.
2X – B = 3D
1  3
D
9  1
BC – 2A
6
4
7. Solve the matrix equations for x and y:
a.
 x  2   y  8
4


  6 2   2 y 8 
c.
2 3
L
M
1 y
N
b.
2 y
 4

 2
 x
 

x
 x
 y   7

5   7
y 8O
L
4 14 O
O
L
M
P
1

y

P
M
M
P
 2Q
0 9 P
N
M
1 1 P
N
Q Q
x
8. Write the augmented matrices for the following systems, then solve using Guassian Elimination.
a.
3x  4 y   6
x  y 5
b.
3x  2 y  7
2 x  3 y  57
9. Use multiplication to determine if the following matrices are inverses of each other:
a.
 1 1 
3
 and B = 
2
 2 3 
A= 
1

1 
b.
4 1 
 and D =
7 2 
C= 
1
 2
  7  2


3
8
10. Find the inverse matrix for the following if possible:
a.
 2 1
 4 3

0
2
b.
4  3
5  2


c.
 1 3
 2 6 


11. Write the matrix equation for each of the following then solve manually.
a.
2x  y  9
b.
5 x  2 y  27
 3x  4 y  5
2 x  y  10
12. Solve the following for matrix X, manually.
a.
 7  5
X
4
3 

8  2 9  3
6 1   6 2

 

b.
 1 0
  6 2   X 


10 6
4 12

8
2
13. Write the matrix equations for the following systems then solve.
8 y  10 z  23
x  y  z  10
a.
5x  y  1
3x  4 y  z  8
b.
6 y  12 z  14
 9 x  5z  0
14. The sum of three numbers is 318. The sum of the first two equals the third. Three times the second is 3 less than twice
the first. Find the three numbers.