3. Consider the following linear system: AZ =7, %3D where 1 1 1 - 1 and (a) What is the dimension of the column space of A? (b) Find a basis for the column space of A.f (c) Without using Gauss Jordan elimination i.e., without considering the augumented ma- trix and bringing it to echolen form, argue that this system does not have any solution i.e., it is incosistent.
3. Consider the following linear system: AZ =7, %3D where 1 1 1 - 1 and (a) What is the dimension of the column space of A? (b) Find a basis for the column space of A.f (c) Without using Gauss Jordan elimination i.e., without considering the augumented ma- trix and bringing it to echolen form, argue that this system does not have any solution i.e., it is incosistent.
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
Pls solve parts a-c
Transcribed Image Text:3. Consider the following linear system:
AT = 7,
where
1
1
A =
1
- 1
2
and
(a) What is the dimension of the column space of A?
(b) Find a basis for the column space of A.f
(c) Without using Gauss Jordan elimination i.e., without considering the augumented ma-
trix and bringing it to echolen form, argue that this system does not have any solution
i.e., it is incosistent.
(d) Leaving the first and second entry ( component ) in 6 as it is, how exactly the third
entry should be changed to make this system consistent?
(e) Again, without using Gauss Jordan elimination, what exactly will be the solution after
the proposed change from last part.,
(f) Now we consider the corresponding homogenous system by putting 6 = 0. Again,
without using Gauss Jordan, argue that the homegneous system will have non-trivial
solutions.
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