Fundamentals of Engineering Analysis EGR 1302 Unit 1, Lecture G
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Transcript of Fundamentals of Engineering Analysis EGR 1302 Unit 1, Lecture G
Slide 1 © 2005 Baylor University
Fundamentals of Engineering AnalysisEGR 1302 Unit 1, Lecture G
Approximate Running Time - 20 minutesDistance Learning / Online Instructional Presentation
Presented byDepartment of Mechanical Engineering
Baylor University
Procedures:
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Slide 2 © 2005 Baylor University
22
533
3
321
321
321
xxx
xxx
xxx
2211
5313
3111
1320
4640
3111
13'
3
12'
2 3
rrr
rrr
23'
3 2
1rrr
1000
4640
3111
Compatible and Incompatible Solutions
?1*0 3 ximplies
Note: detA=0
This system has no solution“inconsistent”
Slide 3 © 2005 Baylor University
2211
5313
1111
2
1
2
3,1)
2
3
2
1(
2
3
2
1,264
11
22
3
xx
xx
x
1320
2640
1111
13'
3
12'
2 3
rrr
rrr
0000
2640
1111
23'
3 2
1rrr
2
3
2
12
1
2
3
3
2
1
x
x
x
The Infinite Solution
Change the System
Same Rowoperations
This system has infinite solutions, depending on the value of
0*0 3 ximplies
detA still equals zero
Slide 4 © 2005 Baylor University
The Three General Solutions
k100
10
1
1. Unique = X3 exists as a single value0det A
k000
10
1
2. None = No X3 exists0det A
0000
10
1
3. Infinite = X3 exists as any value0det A
Slide 5 © 2005 Baylor University
Graphic Examples of the Three General Solutions
X Y S( ) Xt Yt P( ) L M N( )
X Y S( ) Xt Yt P( ) L M N( )
X Y S( ) Xt Yt P( ) L M N( )
12734
56312
102102
zyx
zyx
zyx
22
533
1
zyx
zyx
zyx
22
2233
1
zyx
zyx
zyx
585809
585103
585571
100
010
001
0000
10
01
21
23
23
21
1000
010
001
23
21
rref()
rref()
rref()
infinite
unique
no solution
planesparallel,
neverintersect
all planesintersect
on the same line
single pointof intersection
Slide 6 © 2005 Baylor University
0*3
02
0
321
21
321
xxxx
xx
xxx
031
0021
0111
x
0500
0110
0111
x
5det xA
0xAThe Homogeneous Set of Linear Equations
2,0
,0
11
22
3
xx
xx
x
A
cc
bb
aa
xdet
0
0
0
21
21
21
Using Cramer’s rule:
This determinant = 0,
implying 0*det xA
0xEither , a trivial solution, or
0det A , implying infinite solutions
When x=5, infinite solutions exist,otherwise, there is no solution.
rref()
Slide 7 © 2005 Baylor University
Example of the Three General Solutions(Example 12.3 in the Text)
1a1
1
a
bz
ba11
3212
2321
Given13
'3
12'
2 2
rrr
rrr
23
'3 rrr &
1100
1430
2321
ba
)1(3det aA
1. Unique Solution
1b1a3. Infinite Solutions0
0z
1b1a2. No Solutions0
kz
Slide 8 © 2005 Baylor University
This concludes Unit 1, Lecture G
You are now ready to take the Unit 1 Exam