2. Consider the following system of three linear equations in three unknowns: x₁ + x₂ + ax₂ = 1 x₂ + ax₂ + x₂ = 3 [ax₂ + x^₂ + x₂ = 2a where a € R. (a) Find condition on a such that the system has a unique solution. (b) Find condition on a such that the system has no solution. (c) Find condition on a such that the system has many solutions.

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,...
icon
Related questions
Question
2.
Consider the following system of three linear equations in three unknowns:
x₁ + x₂ + ax3 = 1
=
x₁ + ax₂ + x3
[ax₁ + x₂ + x3 =
3,
= 2a
where a € R.
(a) Find condition on a such that the system has a unique solution.
(b) Find condition on a such that the system has no solution.
(c) Find condition on a such that the system has many solutions.
Transcribed Image Text:2. Consider the following system of three linear equations in three unknowns: x₁ + x₂ + ax3 = 1 = x₁ + ax₂ + x3 [ax₁ + x₂ + x3 = 3, = 2a where a € R. (a) Find condition on a such that the system has a unique solution. (b) Find condition on a such that the system has no solution. (c) Find condition on a such that the system has many solutions.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education