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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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 15AEXP
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Pls solve parts a-c
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.
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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