to write the solution set of the given homogeneous parametric vector form. 5. 7. 9. 11. x₁ + 3x₂ + x3 = 0 -4x₁9x2 + 2x3 = 0 - 3x₂ - 6x3 = 0 12. In Exercises 7-12, describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given matrix. 1 0 [ -1 0 0 3 1 0 0 0 3 -3 7 1 -4 5 -9 6 3 -2 -4 -2 0 1 0 0 0 0 0 0 0 0 5 0 2-6 1 -7 000 ✓ 6. 8. 10. ܐܘܘܗ 3 -5 0 -1 1 -4 0 1 9 4 -8 0 1 0 000 0 X₁ + 3x₂ - 5x3 = 0 X₁ + 4x2 - 8x3 = 0 -3x₁ - 7x2 + 9x3 = 0 1 1 2 -2 -9 5 1 2 -6 -4 3 0 60-8 13. Suppose the solution set of a certain system of linear equa- tions can be described as x₁ 5+4x3, x2 = -2 - 7x3, with x3 free. Use vectors to describe this set as a line in R³. 14. Suppose the solution set of a certain system of linear 3X4, X2 = 8 + x4, equations can be described as x₁ x3 = 2-5x4, with x4 free. Use vectors to describe this set as a "line" in R4. 15. Follow the method of Example 3 to describe the solutions of the following system in por
to write the solution set of the given homogeneous parametric vector form. 5. 7. 9. 11. x₁ + 3x₂ + x3 = 0 -4x₁9x2 + 2x3 = 0 - 3x₂ - 6x3 = 0 12. In Exercises 7-12, describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given matrix. 1 0 [ -1 0 0 3 1 0 0 0 3 -3 7 1 -4 5 -9 6 3 -2 -4 -2 0 1 0 0 0 0 0 0 0 0 5 0 2-6 1 -7 000 ✓ 6. 8. 10. ܐܘܘܗ 3 -5 0 -1 1 -4 0 1 9 4 -8 0 1 0 000 0 X₁ + 3x₂ - 5x3 = 0 X₁ + 4x2 - 8x3 = 0 -3x₁ - 7x2 + 9x3 = 0 1 1 2 -2 -9 5 1 2 -6 -4 3 0 60-8 13. Suppose the solution set of a certain system of linear equa- tions can be described as x₁ 5+4x3, x2 = -2 - 7x3, with x3 free. Use vectors to describe this set as a line in R³. 14. Suppose the solution set of a certain system of linear 3X4, X2 = 8 + x4, equations can be described as x₁ x3 = 2-5x4, with x4 free. Use vectors to describe this set as a "line" in R4. 15. Follow the method of Example 3 to describe the solutions of the following system in por
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
9 pl
![to write the solution set of the given homogeneous
parametric vector form.
5.
x₁ + 3x₂ + x3 = 0
-4x₁ - 9x2 + 2x3 = 0
-3x₁7x2 + 9x3 = 0
- 3x₂ - 6x3 = 0
In Exercises 7-12, describe all solutions of Ax = 0 in parametric
vector form, where A is row equivalent to the given matrix.
7.
9.
11.
12.
[6
[-
-1
1
0
0
0
3
1
0
0
0
3 -3
1 -4
-9
6
-_-9]
5
0
0
0
3-2
-4 -2
0
1
0
0
0
0
2
1
0
0
7
5
0
0
0
0
-6
-7
6.
8.
Syster
10.
9 0
4 -8
0
0
1
0 0 0
3
-5
-57
0
-1
1
-4
0 0
x₁ + 3x₂ - 5x3 = 0
HOY
x₁ + 4x28x3 = 0
1
[1
1
[2²2
-2 -9 5
I
_$]
3
6
2 -6
0 -4
0-8
3]
13. Suppose the solution set of a certain system of linear equa-
tions can be described as x₁ = 5+4x3, x2 = -2-7x3, with
x3 free. Use vectors to describe this set as a line in R³.
14. Suppose the solution set of a certain
equations can be described as x₁
system of linear
:3X4, X₂ = 8 + X4,
as a "line" in R4.
x3 = 2 - 5x4, with x4 free. Use vectors to describe this set
15. Follow the method of Example 3 to describe the solutions of](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F065b059c-d698-454e-9c8f-cc5a79a01d3c%2Fb9077671-5581-48e6-bcd3-db62a40287f5%2Fs45kglb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:to write the solution set of the given homogeneous
parametric vector form.
5.
x₁ + 3x₂ + x3 = 0
-4x₁ - 9x2 + 2x3 = 0
-3x₁7x2 + 9x3 = 0
- 3x₂ - 6x3 = 0
In Exercises 7-12, describe all solutions of Ax = 0 in parametric
vector form, where A is row equivalent to the given matrix.
7.
9.
11.
12.
[6
[-
-1
1
0
0
0
3
1
0
0
0
3 -3
1 -4
-9
6
-_-9]
5
0
0
0
3-2
-4 -2
0
1
0
0
0
0
2
1
0
0
7
5
0
0
0
0
-6
-7
6.
8.
Syster
10.
9 0
4 -8
0
0
1
0 0 0
3
-5
-57
0
-1
1
-4
0 0
x₁ + 3x₂ - 5x3 = 0
HOY
x₁ + 4x28x3 = 0
1
[1
1
[2²2
-2 -9 5
I
_$]
3
6
2 -6
0 -4
0-8
3]
13. Suppose the solution set of a certain system of linear equa-
tions can be described as x₁ = 5+4x3, x2 = -2-7x3, with
x3 free. Use vectors to describe this set as a line in R³.
14. Suppose the solution set of a certain
equations can be described as x₁
system of linear
:3X4, X₂ = 8 + X4,
as a "line" in R4.
x3 = 2 - 5x4, with x4 free. Use vectors to describe this set
15. Follow the method of Example 3 to describe the solutions of
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