null space of A, null space of A".
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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Question
![1. Consider
1 2 1
2 5 1
3 7 2
4 9 3
1
A =
2
-2
-1
4
Let
R(A) = column space of A
R(A") = column space of A",
N(A) = null space of A,
N(A") = null space of A".
(a) By finding the linearly independent columns, express the four fundamental spaces:
R(A), R(A"), N(A), and N(A"). Also find their dimensions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5909bef-ac29-4b8c-b4b1-b9f5e26ca729%2F5b921d51-eeef-43b1-b2d3-b9162dbe0822%2Fc9i6ch6_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider
1 2 1
2 5 1
3 7 2
4 9 3
1
A =
2
-2
-1
4
Let
R(A) = column space of A
R(A") = column space of A",
N(A) = null space of A,
N(A") = null space of A".
(a) By finding the linearly independent columns, express the four fundamental spaces:
R(A), R(A"), N(A), and N(A"). Also find their dimensions.
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