FALL 2015
MATH 141 - ASSIGNMENT (2.1-2.5)
DUE: 9/21/15
Name
All steps must be written clearly and neatly to get full credit. If you use your calculator for
anything beyond an arithmetic calculation, please indicate how at the appropriate step.
1. (10pts) Find a, b, and c in the following matrix equation.
!
35 −78
2 3
−4
3
a
−1 4
!T


4c −1
3 −7 2b + 7 
5
=
3

−2 3
1
2 −4
!
Solution:
Transpose:




4c −1
3 −7 2b + 7 
2 −1
35 −78
5
=
−4

3
−2 3
1
3 4
3
a
2 −4
Scalar multiplication:
!
!
!
4c −1
35 −78
8 −4
3 −7 2b + 7 
5
−
=

3
3
a
12 16
−2 3
1
2 −4
!
Subtraction:
!
!


4c −1
27 −74
3 −7 2b + 7 
5
=

3
−9 a − 16
−2 3
1
2 −4
!
!
Multiplication:
!
27 −74
3(4c) + (−7)(3) + (2b + 7)(2) 3(−1) + (−7)(5) + (2b + 7)(−4)
=
−2(4c) + 3(3) + 1(2)
−2(−1) + 3(5) + 1(−4)
−9 a − 16
12c − 7 + 4b −66 − 8b
=
−8c + 11
13
!
a − 16 = 13 so a = 29.
−66 − 8b = −74 so b = 1.
−8c + 11 = −9 so c = 2.5.
1
!
2
ASSIGNMENT (2.1-2.5)
2. The body of Alisha was discovered in the basement of the company where she worked.
The medical examiner determined that she was killed between 9 p.m. and 10 p.m. After a
preliminary investigation, homicide detectives decided to question three of her coworkers: Alex,
Bob, and Charlie.
The detectives were told by the suspects that Alex left work at 9:18 p.m. on the day of the
homicide, walked 1000 ft to his car, and drove 16 mi to his house, arriving home at 9:40 p.m.
Bob left work at 9:12 p.m., walked 400 ft to his car, and drove 12 mi to his house, arriving
home at 9:30 p.m.
Charlie punched out at 9:35:30 p.m., walked 600 ft to his car, and drove 20 mi to his house,
arriving home at 10 p.m.
The three suspects walked at an average speed of v ft/sec, and drove at an average speed of
w ft/sec.
After analyzing the information above, the detectives singled out Bob for further questioning.
(i) (7pts) Let x = v1 and let y = w1 . Based on the information given, set up a system of
three linear equations in terms of x and y.
(You may want to write (nonlinear) equations in terms of v and w first, using the
relations 1 mi = 5280 ft, and Distance
=Time.)
Speed
(ii) (4pts) Solve the system of linear equations.
(iii) (4pts) Find the solution for each possible pair of equations in the system, and explain
why the detectives singled out Bob.
Solution: (i) In terms of v and w:
1000 84480
+
= 1320
v
w
400 63360
+
= 1080
v
w
600 105600
+
= 1470
v
w
In terms of x and y:


1000x + 84480y = 1320
(1)
400x + 63360y = 1080
(2)
600x + 105600y = 1470
(3)


1000 84480 1320
1 0 0
 rref 
400 63360 1080  →  0 1 0 
(ii)

600 105600 1470
0 0 1
No solution.
(iii) The easiest way may be to find the intersection point using the graphing calculator. The
rref command can also be used.
9 23
Eq. 1 and Eq. 2: (-0.2571, 0.01867). Alternatively, in fractions, (− ,
).
35 1232
99
5
Eq. 2 and Eq. 3: (4.95, -0.0142). Alternatively, in fractions, ( , −
).
20 352
18 113
Eq. 1 and Eq. 3: (0.2769, 0.01235). Alternatively, in fractions, ( ,
).
65 9152
Only the solution from the first and third equations makes sense since x and y cannot be
negative. In other words, the information about Bob does not tally with the information about
either Alex or Charlie.

