3. Consider the following linear system: A7 = 3, where 1 A = 1 1 and (a) What is the dimension of the column space of A? (b) Find a basis for the column space of A. (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 7 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.
3. Consider the following linear system: A7 = 3, where 1 A = 1 1 and (a) What is the dimension of the column space of A? (b) Find a basis for the column space of A. (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 7 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.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 3CEXP
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Pls solve parts d e f
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04fde401-d1f2-4e8b-bd38-00484399c59b%2Fb0224688-bad5-497e-8263-0ff808ced86a%2Fivs5z4_processed.jpeg&w=3840&q=75)
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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