Name:
Period:
C
College Algebra: Ch.10.1-10.4 Test
In problems 1 - 5, choose the one alternative that best completes the statement or answers the question.
Supporting work/reasoning must be shown in order to receive credit for your answer.
  1 2  5
  5  3  7 

1. Perform the matrix multiplication. 
    1  2  6
3

2
6

  4  4  1


 20 23 
 20 24
50 
50 
 30 24
 24  14  C)  20 24
A) 
B)
D) 





 23  14  9 
 23  14  9 
 29  14
 50
 9 
2. Solve the system.
A)
B)
C)
D)
E)
 1 2 , 7 2
1 2 , 2
 1 2 ,  2
 1, 1 2
1. ______(+2)
50 
E) none of these
 9 
 4 x  4 y  6
2 x  8 y  17
2. ______(+2)
none of the above
4
 3 3
0
3. Let A  
and B  

 . Find 2A + 3B.
2 5
 1 6 
 6 18 
 6 18 
 6 12 
A) 
B) 
C) 



 7 28
 1 28
 1 28 
3. ______(+2)
6
D) 
3
7
18
E) none of these
4. A flat rectangular piece of aluminum has a perimeter of 72 inches. The width is 12 inches
4. ______(+2)
longer than the length. Find the width.
A)
B)
C)
D)
E)
24 inches
18 inches
10 inches
12 inches
none of the above
5. Solve for x.
5
2
A) 3
B) -3
C) 18
D) 4
E) none of the above
x
3
  21
5. ______(+2)
6. Solve by Cramer's Rule the following system of linear equations. Clearly state all determinants formed to
compute your final solution.
2x  y  2z  11
4 x  3y  z  9
 6x  5y  3z  16
(x,y,z) = ____________________
D = ________ Dx = ________
Dy = ________ Dz = ________
7. Determine the Inverse of the matrix A. Clearly state all work required to produce the complete row echelon
form and execute one row operation per table entry. Write your final answer in the matrix space provided.
Reduce all improper fractions.
1 1 0 
A   3 0 1 
 5 3  2
Row Operation
A 1
Arithmetic Work







Resulting Matrix







8. Solve the following system of linear equations by Algebraic Elimination, Cramer’s Rule, or Matrices. If
applicable, give answers as reduced improper fractions. No decimal answers will be accepted.
3x  2 y  7 z  4
 4 x  3y  4z  5
6x  5y  4z  8
(x,y,z) = _____________________