Given the matrix A and the vectors X and b such that: 中 [1-1 15 X2 24 3 13 x=x, and b: b, b. A = 4 3-3 1 4 [7 9 -24 7 22 X4. a) Find a basis of the null-space of A. b) If b-[163 93 29 86], find all the solutions of the equation Ax b. c) If b-[0 4 7 8. does the equation Ax b have solutions? Justify your answer. d) If b [b b, b, b.]. find the relationship between b. b,. b, and b, such that the equation Ax = b is solvable.
Given the matrix A and the vectors X and b such that: 中 [1-1 15 X2 24 3 13 x=x, and b: b, b. A = 4 3-3 1 4 [7 9 -24 7 22 X4. a) Find a basis of the null-space of A. b) If b-[163 93 29 86], find all the solutions of the equation Ax b. c) If b-[0 4 7 8. does the equation Ax b have solutions? Justify your answer. d) If b [b b, b, b.]. find the relationship between b. b,. b, and b, such that the equation Ax = b is solvable.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Given the matrix A and the vectors X and b such that:
中
[1 -1
15
X2
2 4
3 13
x= x, and b:
b,
b.
A=
4
3-3
1
4
[7
9 -24
7 22
X4.
a) Find a basis of the null-space of A.
b) If b-[163 93 29 86], find all the solutions of the equation Ax b.
c) If b-[0 4 7 8. does the equation Ax b have solutions? Justify your answer.
d) If b [b b, b, b.]. find the relationship between b. b,. b, and b, such that the equation
Ax = b is solvable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7976f1a-12bb-4fe1-8e69-448573c6f064%2Fc54a9f0b-682c-4f8b-9056-84a7225ead81%2F66x752_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given the matrix A and the vectors X and b such that:
中
[1 -1
15
X2
2 4
3 13
x= x, and b:
b,
b.
A=
4
3-3
1
4
[7
9 -24
7 22
X4.
a) Find a basis of the null-space of A.
b) If b-[163 93 29 86], find all the solutions of the equation Ax b.
c) If b-[0 4 7 8. does the equation Ax b have solutions? Justify your answer.
d) If b [b b, b, b.]. find the relationship between b. b,. b, and b, such that the equation
Ax = b is solvable.
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