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1.
Chapter 1 Review
Find the following, if possible. If not possible, explain why.
 1  1
3 2 
 4 0
2
A
B

D  2 5
C

0 

 2 1 

5

1




 4
3 
a) -5A
f) B-1
b) B + D
g) det A
c) B – 2A + 3I
h) A2
Solve each matrix equation for X:
2 7 
 5 0
a) 10X  
  2 1 6
8

4




d) A  C
i) A  B
e) D  B
j) B  A
2.
2
8
6 
b) 
 X   6

5

1


 
3. Solve each system using matrices:
a) without a graphing calculator
3x  9y  3
b) with a graphing calculator
4x  6y  144
b) with a graphing calculator
3y  z  8x  14
 2y  8  x
5x  2y  66
7x  3y  z  29
2z  20  6x
Steve’s long distance phone charges for three months were as follows:
Month
Canada minutes
USA minutes
Overseas minutes
June
17
25
10
July
17
33
0
August
15
8
19
Using a matrix equation, find the per minute charge for calls within Canada, to the USA and to Europe.
4.
Charges ($)
15.69
10.81
17.39
5.
Kyle is thinking of three numbers. The sum of all three numbers is 52. The largest number is four times bigger than the smallest
number. The smallest number is four less than the middle number. Find Kyle’s numbers.
6.
When a football is kicked, it goes up into the air, reaches a maximum altitude, and then
comes back down. Assume that a quadratic function is a reasonable mathematical model
for this real-world situation.
t = the number of seconds that have elapsed since the ball was punted
d = number of feet the ball is above the ground
a) Find the quadratic equation that describes the height of the ball with respect to time.
b) How high is the ball 1.5 seconds after it is punted?
1.
Chapter 1 Review
Find the following, if possible. If not possible, explain why.
 1  1
3 2 
 4 0
A
B
D  2 5
C   2
0 


5

1

2
1




 4
3 
a) -5A
f) B-1
b) B + D
g) det A
c) B – 2A + 3I
h) A2
Solve each matrix equation for X:
2 7 
 5 0
 2
a) 10X  


8  4 
 1 6
d) A  C
i) A  B
T (s)
0
1
2
D(ft)
4
28
20
e) D  B
j) B  A
2.
2
8
6 
X 
b) 

 5  1
 6
3. Solve each system using matrices:
a) without a graphing calculator
3x  9y  3
b) with a graphing calculator
4x  6y  144
b) with a graphing calculator
3y  z  8x  14
 2y  8  x
5x  2y  66
7x  3y  z  29
2z  20  6x
Steve’s long distance phone charges for three months were as follows:
Month
Canada minutes
USA minutes
Overseas minutes
June
17
25
10
July
17
33
0
August
15
8
19
Using a matrix equation, find the per minute charge for calls within Canada, to the USA and to Europe.
4.
Charges ($)
15.69
10.81
17.39
5.
Kyle is thinking of three numbers. The sum of all three numbers is 52. The largest number is four times bigger than the smallest
number. The smallest number is four less than the middle number. Find Kyle’s numbers.
6.
When a football is kicked, it goes up into the air, reaches a maximum altitude, and then
comes back down. Assume that a quadratic function is a reasonable mathematical model
for this real-world situation.
t = the number of seconds that have elapsed since the ball was punted
d = number of feet the ball is above the ground
a) Find the quadratic equation that describes the height of the ball with respect to time.
b) How high is the ball 1.5 seconds after it is punted?
T (s)
0
1
2
D(ft)
4
28
20
Answers:
1. a)
  15  10
 25
5 

g) -13
b) not
possible
h)
19 4 
10 11


c)
 4
 1
 12 6 


d) not
possible
i)
2
8
22  1


j)
 12 8 
 1  5


e)  2
2.a)
5
1.2 0.7
 0. 6 0. 8 


 1 0
4

 1 1
2

3
b)  
 9
f)
3.a) (x, y) = (26, -9)
b) (x, y) = (18, 12)
c) (x, y, z) = (1, 5, -7)
4. $0.17 within Canada, $0.24 to 5. Kyle’s numbers are 8, 6. a) d  16t2  40t  4
USA and $0.68 overseas
12, and 32
b) 28 ft