1. Consider1 2 12 5 13 7 24 9 31A =2-2-14LetR(A) = column space of AR(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.

We have to find out the four fundamental spaces and their dimensions.

Answered: null space of A, null space of A".

Math

Advanced Math

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.

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