NAME_____________________________________________________________________________________________________
MAYNARD
MATH 115
TEST 5
CHAPTER 16 & 18
SAMPLE
1)
Evaluate by expansion by minors.
(418:5)
6
1
2
10
2 3
1 2
3
2)
Evaluate by expansion by minors.
(418:9)
1 0 1 0
2 4 3 1
1 1
3 5
1
0
1
2
3)
Evaluate by expansion by minors.
(418:13)
1 2 1 2 1
1 0 0 1 0
0 1 1 0 1
1 1 2 2 1
0 1 1 0 2
4)
Solve the system of equations by determinants (Cramer's Rule).
(418:21) Evaluate the determinants by expansion by minors.
xt=0
3x  y  z = 1
2y  z  3t = 1
2z  3t = 1
5)
Evaluate the determinant by inspection, without any calculations.
(422:1)
4 5
0
0
3
0
8
8
5
6)
Evaluate the determinant by inspection, without any calculations.
(422:5)
 2 0 1
5 0 3
3 0 4
7)
Evaluate the determinant by using elementary row operations and the
(422:17) properties of determinants.
1 3 3
4 2 1
5
2
3 2 2 2
0 1 2 1
8)
Add the matrices.
(427:9)
 2 3  1 7 

  

  5 4  5  2
9)
Let
(427:17)
and
 1 4  7 0

A  
 2  6 1 2
1 5  6 3 
.
B  
 4 1 8  2
10)
Multiply.
(432:9)
Find 2A  B
 1 7 


5  2 1 
 3
 10  1 5  3 



  5 12 


11)
Determine whether or not B = A1
(432:23)
 1 2 3 


A   2 5 7 
  1 3  5


 4 1 1 


B   3  2  1
 1  1  1


12)
Determine by matrix multiplication whether or not A is the
(432:25) correct matrix of solution values.
3x  2y = 1
4x  y = 6
1
A   
 2
13)
Find A1.
(436:1)
 2  5

A  
 2 4 
1
14)
Find A .
(436:21)
3
2
 1


A    2  5  1
 2
4
0 

15)
Solve the system of equations using the inverse of the coefficient matrix.
(440:1) (Use the inverse from 13) above.)
2x  5y = 14
2x  4y = 11
16)
Solve the system of equations using the inverse of the coefficient matrix.
(440:7) (Use the inverse from 14) above.)
x  3y  2z = 5
2x  5y  z = 1
2x  4y = 2
17)
Express the ratio in the simplest form.
(472:5)
20 qt to 2.5 gal
18)
In testing for quality control, it was found that 17
(472:37) of every 500 computer chips produced by a
company in a day were defective. If a total of 595
defective parts were found, what was the total
number of chips produced during that day?
19)
The force F on the blade of a wind generator
(478:37) varies jointly as the blade area A and the
square of the wind velocity v. Find the
equation relating F, A, and v if F = 19.2 lb
when A = 3.72 ft2 and v = 31.4 ft/s.
20)
The power gain G of a parabolic microwave
(478:45) dish varies directly as the square of the
diameter d of the opening and inversely as the
square of the wavelength  of the wave carrier.
Find the equation relating G, d, and 
if G = 5.5 x 104 for d = 2.9 m and  = 0.030 m.
ANSWERS
1) 50
2) 6
3) 2
4) x = 1, y = 0, z = 2, t = 1
5) 60
6) 0
7) 72
8)
 1 10 


0 2 
9)
  1 13  20 3 


6
2 
 8  13
 33  22 


10)  31  12 
 15 13 


 50  41 


11) Yes, B = A1
12) yes
13) A
1

2


 1
5

2 
1 
15) x = 1/2, y = 3
16) x = 1, y = 0, z = 3
17) 2
18) 17,500 chips
19) F = 0.00523 Av2
20) G 
5.9d 2
2

4
2

1
14) A    1  2


1
1

7 

2 
3
2 
1 

2 