x+y +2 =0 y+2z -4 x - -10 [10 -1 4] 01 2 4+ 01 2 4 01 2 4 01 2 4-0 1 2 0 0 0 0 14 10 -1 -4] 10 -1 0 10 -1 10 0 -1 -2 10 Lo 0 0 1 0 0 0 1 Therefore, we have an inconsistent system (no solution). 20 io à 3. Show that the following system has infinitely many solutions. * + y + 100 5x + 10y + 20z = 2000 -5x + 10z = 1000 [111 100 [111 100] [111 100 5 10 20 2000 -0 5 15 1500 -0 1 3 300 -0 1 3 05 15 1500 10 -2 -200 300 -5 0 10 1000 OS 15 1500 0 0 0 0 2z-200 Solutions: 300-32
x+y +2 =0 y+2z -4 x - -10 [10 -1 4] 01 2 4+ 01 2 4 01 2 4 01 2 4-0 1 2 0 0 0 0 14 10 -1 -4] 10 -1 0 10 -1 10 0 -1 -2 10 Lo 0 0 1 0 0 0 1 Therefore, we have an inconsistent system (no solution). 20 io à 3. Show that the following system has infinitely many solutions. * + y + 100 5x + 10y + 20z = 2000 -5x + 10z = 1000 [111 100 [111 100] [111 100 5 10 20 2000 -0 5 15 1500 -0 1 3 300 -0 1 3 05 15 1500 10 -2 -200 300 -5 0 10 1000 OS 15 1500 0 0 0 0 2z-200 Solutions: 300-32
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 10EQ
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Wed Sep 8 7:11 PM
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Bb LEARN X
Bb Math 2 X
Bb Math 2 X
solving X
How T X
Solving X
How T X
Deepl X
buenos X
spanis x
Membe X
Мy Qu X
gauss
X G gauss
Gaussi X
> Algebr X
farmingdale.open.suny.edu/bbcswebdav/pid-2193589-dt-content-rid-22841230_1/courses/202109-MTH245-001-90761/MTH%20245%20Solving%20Systems.pdf
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100%
x +y +z = 0
Ety
Wndng dm a
y+2z = 4
ntem te
2
W a
z =10
1
1
1
[1
1
1
[1 0 -1 -4
[1 0 -1 -4]
1 0 -1 0
0 1
4 →|0
1
2
4
1
2
4
→|0 1
2
4 →0 1
2
1
0 -1 10
0 -1 -2 10
14
0 0
1
0 0
1
Therefore, we have an inconsistent system (no solution).
I a
..M ... ...
10
30
10
- 10
-20
20
10
-30
-40
20
io
10
10 20
3. Show that the following system has infinitely many solutions.
+ y
+ z =
100
5x + 10y + 20z = 2000
-5x
10z = 1000
1 1 1 100
1 1 1
100
1 1 1 100
1 0 -2 -200
10 20
2000 → 0 5 15 1500→ 0 1
3
300
→ 0 1
3
300
-5 0
10
1000
0 5 15 1500
0 5 15 1500
|0 0 0 0
6.
2z - 200
Solutions:
y
300 – 3z
Cur Fining
國TO
SEP
PAGES
8.
101
0000
II](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7daa69d8-205a-4b72-abf5-96966d755823%2Fe52ac471-e0ae-4d57-aefd-fafdd6bb49e8%2Frjkt4ye_processed.png&w=3840&q=75)
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Wed Sep 8 7:11 PM
History X
FSC myFSC X
Bb LEARN X
Bb Math 2 X
Bb Math 2 X
solving X
How T X
Solving X
How T X
Deepl X
buenos X
spanis x
Membe X
Мy Qu X
gauss
X G gauss
Gaussi X
> Algebr X
farmingdale.open.suny.edu/bbcswebdav/pid-2193589-dt-content-rid-22841230_1/courses/202109-MTH245-001-90761/MTH%20245%20Solving%20Systems.pdf
27
* ES
Apps
Reading List
Math 245
4 / 10
100%
x +y +z = 0
Ety
Wndng dm a
y+2z = 4
ntem te
2
W a
z =10
1
1
1
[1
1
1
[1 0 -1 -4
[1 0 -1 -4]
1 0 -1 0
0 1
4 →|0
1
2
4
1
2
4
→|0 1
2
4 →0 1
2
1
0 -1 10
0 -1 -2 10
14
0 0
1
0 0
1
Therefore, we have an inconsistent system (no solution).
I a
..M ... ...
10
30
10
- 10
-20
20
10
-30
-40
20
io
10
10 20
3. Show that the following system has infinitely many solutions.
+ y
+ z =
100
5x + 10y + 20z = 2000
-5x
10z = 1000
1 1 1 100
1 1 1
100
1 1 1 100
1 0 -2 -200
10 20
2000 → 0 5 15 1500→ 0 1
3
300
→ 0 1
3
300
-5 0
10
1000
0 5 15 1500
0 5 15 1500
|0 0 0 0
6.
2z - 200
Solutions:
y
300 – 3z
Cur Fining
國TO
SEP
PAGES
8.
101
0000
II
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