3. Given the following system: x, - 2x, + 2x, + 3x, = -1 -3x, + 6x, + x, + 5x, =-11 2x, %3D 4x, 2x, 6x, = 10 (a) Explain why the system is non-homogeneous. (b) Find the reduced row echelon form (RREF) of the augmented matrix representing the above system and describe the solution for (x,.X,,) from the RREF. Deduce the solution in parametric form. (c) Use the theory on solutions to systems of linear equations to justify that the solution you deduced above is correct (use whichever convention you prefer).

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter6: Matrices And Determinants
Section: Chapter Questions
Problem 4CC
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Question
3.
Given the following system:
2x, + 2x, + 3x, = -1
-3x, + 6x, + x, + 5x, = -11
6x, = 10
2x,
4x;
2x,
(a) Explain why the system is non-homogencous.
(b) Find the reduced row echelon form (RREF) of the augmented matrix representing the
above system and describe the solution for (x,.,X,x) from the RREF. Deduce the
solution in parametric form.
(c) Use the theory on solutions to systems of lincar equations to justify that the solution you
deduced above is correct (use whichever convention you prefer).
(d) If the convention used for the system above is 4-v=b, express its associated
homogeneous system. Deduce the basis of the null space of 4 based on the results you
obtained.
Transcribed Image Text:3. Given the following system: 2x, + 2x, + 3x, = -1 -3x, + 6x, + x, + 5x, = -11 6x, = 10 2x, 4x; 2x, (a) Explain why the system is non-homogencous. (b) Find the reduced row echelon form (RREF) of the augmented matrix representing the above system and describe the solution for (x,.,X,x) from the RREF. Deduce the solution in parametric form. (c) Use the theory on solutions to systems of lincar equations to justify that the solution you deduced above is correct (use whichever convention you prefer). (d) If the convention used for the system above is 4-v=b, express its associated homogeneous system. Deduce the basis of the null space of 4 based on the results you obtained.
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