Consider the following system of linear equations.2.т + Зу 3 1х — у — 2Зл — 2у — — 1= -(a) Before solving the system, give a brief geometric description of its solution set.(b) By hand, find the RREF of the augmented matrix of the system, indicating the rowoperations you are using at each step.(c) Is the system consistent?(d) Find the solution set of the system.

Answered: Consider the following system of linear…

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

Consider the following system of linear equations.
2.т + Зу 3 1
х — у — 2
Зл — 2у — — 1
= -
(a) Before solving the system, give a brief geometric description of its solution set.
(b) By hand, find the RREF of the augmented matrix of the system, indicating the row
operations you are using at each step.
(c) Is the system consistent?
(d) Find the solution set of the system.

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The following definitions are used to obtain the required solution.

If a system of linear equations has at least one solution, then the system is said to be consistent.
If a system of linear equations has no solution, then the system is said to be inconsistent.
If a system of linear equations has an infinite number of solutions, then the system is said to be dependent.