MAC 1140 - Test 4 Practice
Name __________________________________
NON-CALCULATOR WORK:
 2 4 
Given A = 

1 3 
 4 1
B= 

2 0 
4
C=  
3
0
 3 2
E= 

 1  1  2
D = 3 1
Calculate. If not possible, put undefined:
2 4
1) A + B
2) 3B
3) AC
4)
5) AE
6) AD
7) B + D
8) B – 2A
1
3
Perform the following row operations beginning with matrix A and using your answer to each problem as the
matrix for the next.
9) –2R2 + R1  R1
11) 
10) R1  R2
1
R2
10
1 6 5 
__________ 12) Given the matrix  2 3 1  calculate the determinant.


0 2 4 
Show your work.
1 3 1 8 


____________________13) Given that the augmented matrix 0 3 1 11 represents a system of
0 0 4 8 
equations, give the solution to the system of equations as an ordered triplet.
14. a. Solve the following system algebraically:
b. Use Gaussian Elimination to solve the following system:
x – 2y + 3z = 4
2x + y – 4z = 3
-3x +4y - z = -2
On Problems 15 and 16, use Cramer’s Rule (determinants) to solve.
15. 2x – 3y = -4
5x + 7y = 1
16. 5x + 2y – z = -7
x – 2y + 2z = 0
3y + z = 17
SOLVE using Gaussian Elimination:
17. -2x + 3y – z = -1
x – 2y + z = 3
18. -2x + 3y – z = 4
2x – 3y + z = 1
19.
x+y–z=0
3x – y + 3z = -2
x + 2y – 3z = -1
For 20 - 21, find the first four terms of each sequence. Then, for 20 - 23 identify each sequence as arithmetic,
geometric, or neither. If arithmetic, identify common difference. If geometric, identify common ratio.
20. an  3n
21. an  n  5
22.
1 1
, ,1,4,...
6 3
1 1
23. 4,1, , ,...
4 16
Arithmetic Sequences
24. Given a1 = 5 and d = -3, find the first four terms of the arithmetic sequence.
25. Given the sequence 3, 6, 9, 12, . . . . write the formula for the nth term.
26. Find a18 in the sequence in exercise 25.
27. Find the sum of the first 10 terms of the arithmetic sequence if a1 = -1 and d = 3
Evaluate the following:
6
5
28.
4
29.
i 1
3
2 j  3
30.
 k!
k 0
j 3
Write the following arithmetic series using summation notation:
32. 4 + 1 – 2 – 5 – 8 – 11 – 14
31. 2 + 7 + 12 + 17 + 22
Find the sum of each arithmetic series.
33. 4 + 1 – 2 – 5 . . . . . – 32
34. 1 
3
5
15
 2   ..... 
2
2
2
21
35.
i 1
Geometric Sequences
36. Identify the terms of the geometric sequence: an  5(3) n1
i  2
1 n  4
Write a formula for the nth term of each geometric sequence.
37. .7, .07, .007, .0007 …….
38. Write the geometric series in summation notation: 3  9  27  81  243  729
Find the sum of the geometric series in 39 - 41.
39. 2  6  18  54  162

40.
 300(0.99)
i
(Note that this is a geometric series. Write the first few terms to confirm this.
i 0
Determine a1 , r, and n then apply formula)
41. 1  1  1 .........
2
4
42. Find the sum of the series (what kind is this one?): 5 + 1 – 3 – 7, …, -27
CALCULATOR WORK. YOU MAY USE A CALCULATOR ON THIS PART:
____________________1) Give the solution to the system of equations as an ordered triplet:
2 x 3 y  z  10
x
3z  6
5 x 2 y
 13
5 x 2 y 3z  1
2 - 3) Given the system of equations: 3x 4 y 2 z  7
7 x 2 y  z  5
__________ 2a) Calculate D
__________ 2b) Calculate Dy
_______________ 3)
4) Solve:
What is the exact value of y in the solution to the system?
x +y+z=4
-2x - y + 3z = 1
y + 5z = 9
ANSWERS TO PRACTICE FOR TEST 4:
6  5
12  3
 4
1. 
2.
3.
 13  4. 10

6 0 
 
3 3 


0 7 
0  10
8. 
9. 

3 
1
0  6 
3 
1
10. 

0 10
8
 10 8
5. 
6. Undefined
 1  6
 0
1 3
11. 

0 1
12. –18
7. Undefined
13. (1, 3, 2)
 25 22 
15.   ,  16. (-2, 4, 5) 17. (x, x + 2, x + 7) or (z – 7, z – 5, z) 18. No solution
 29 29 
19. (-2, 5, 3) 20. 3, 9, 27, 81 Geometric; r = 3
21. 6, 7, 8, 9 Arithmetic; d = 1
22. Neither
5
1
23. Geometric; r 
24. 5, 2, -1, -4 25. an = 3n 26. 54 27. 125 28. 20 29. 24 30. 10 31.  5i  3
4
i 1
6
7
119
32.   3i  7 33. -182 34.
35. 273 36. 5, 15, 45, 135 37. an  0.7(01
. ) n1 38.  3( 3) n 1
2
i 1
n 1
39. 242 40. 30,000 41. 2
42. -99
14. (4, 3, 2)
CALCULATOR PART:
1. (3, 1, -1)
2a. –44
2b. –288
3.
72
11
4. { (4z – 5, -5z + 9, z)| z is a real number}