3. Given the following system: + 3x, + 5x, 2x, + 2x, -1 -3x, + 6x, + X3 -11 %3D 2x, 4х, 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,,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). (d) If the convention used for the system above is A v=b, express its associated homogeneous system. Deduce the basis of the null space of A based on the results you obtained.

3. Given the following system: + 3x, + 5x, 2x, + 2x, -1 -3x, + 6x, + X3 -11 %3D 2x, 4х, 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,,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). (d) If the convention used for the system above is A v=b, express its associated homogeneous system. Deduce the basis of the null space of A based on the results you obtained.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

3.
Given the following system:
2.x, + 2x, + 3x,
-1
-3x, + 6x, +
+ 5x,
-11
%3D
2x,
4х,
2x,
6x,
10
%3D
(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,,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).
(d) If the convention used for the system above is A v=b, express its associated
homogeneous system. Deduce the basis of the null space of A based on the results you
obtained.

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