UPSC Exam  >  UPSC Questions  >  Suppose  Consider the following system of lin... Start Learning for Free
Suppose  Consider the following system of linear equations. x + y + z = α, x + βy + z = γ, x + y + αz = β. If this system has at least one solution, then which of the following statements is (are) true? a)If α = 1 then γ = 1 b)If β = 1 then γ = α c)If β  ≠ 1 then α = 1 d)If γ = 1 then?
Most Upvoted Answer
Suppose  Consider the following system of linear equations. x + y + z ...
Analysis of the System of Equations
The given system of equations is:
1. \( x + y + z = \alpha \)
2. \( x + \beta y + z = \gamma \)
3. \( x + y + \alpha z = \beta \)
To determine the conditions under which this system has at least one solution, we can set up a matrix and check for consistency.
Condition for Consistency
For the system to have at least one solution, the determinant of the coefficient matrix should be zero or the augmented matrix must be consistent.
Evaluating the Statements
- a) If α = 1 then γ = 1
- This statement is not necessarily true. The values of γ depend on the coefficients and do not directly imply that if α = 1, then γ must also equal 1.
- b) If β = 1 then γ = α
- This statement is true. Substituting β = 1 into the second equation leads to γ = α, confirming the relationship.
- c) If β ≠ 1 then α = 1
- This statement is not necessarily true. The value of α can vary independently of β, thus α does not have to equal 1 when β is not equal to 1.
- d) If γ = 1 then?
- This statement is incomplete. However, if γ = 1, it does not provide sufficient information about α or β without additional context or constraints provided by the other equations.
Conclusion
In summary, the only definitive statement that holds true under the conditions laid out is b. The other statements either lack sufficient justification or are not universally applicable.
Explore Courses for UPSC exam

Top Courses for UPSC

Suppose  Consider the following system of linear equations. x + y + z = α, x + βy + z = γ, x + y + αz = β. If this system has at least one solution, then which of the following statements is (are) true? a)If α = 1 then γ = 1 b)If β = 1 then γ = α c)If β  ≠ 1 then α = 1 d)If γ = 1 then?
Question Description
Suppose  Consider the following system of linear equations. x + y + z = α, x + βy + z = γ, x + y + αz = β. If this system has at least one solution, then which of the following statements is (are) true? a)If α = 1 then γ = 1 b)If β = 1 then γ = α c)If β  ≠ 1 then α = 1 d)If γ = 1 then? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Suppose  Consider the following system of linear equations. x + y + z = α, x + βy + z = γ, x + y + αz = β. If this system has at least one solution, then which of the following statements is (are) true? a)If α = 1 then γ = 1 b)If β = 1 then γ = α c)If β  ≠ 1 then α = 1 d)If γ = 1 then? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose  Consider the following system of linear equations. x + y + z = α, x + βy + z = γ, x + y + αz = β. If this system has at least one solution, then which of the following statements is (are) true? a)If α = 1 then γ = 1 b)If β = 1 then γ = α c)If β  ≠ 1 then α = 1 d)If γ = 1 then?.
Solutions for Suppose  Consider the following system of linear equations. x + y + z = α, x + βy + z = γ, x + y + αz = β. If this system has at least one solution, then which of the following statements is (are) true? a)If α = 1 then γ = 1 b)If β = 1 then γ = α c)If β  ≠ 1 then α = 1 d)If γ = 1 then? in English & in Hindi are available as part of our courses for UPSC. Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of Suppose  Consider the following system of linear equations. x + y + z = α, x + βy + z = γ, x + y + αz = β. If this system has at least one solution, then which of the following statements is (are) true? a)If α = 1 then γ = 1 b)If β = 1 then γ = α c)If β  ≠ 1 then α = 1 d)If γ = 1 then? defined & explained in the simplest way possible. Besides giving the explanation of Suppose  Consider the following system of linear equations. x + y + z = α, x + βy + z = γ, x + y + αz = β. If this system has at least one solution, then which of the following statements is (are) true? a)If α = 1 then γ = 1 b)If β = 1 then γ = α c)If β  ≠ 1 then α = 1 d)If γ = 1 then?, a detailed solution for Suppose  Consider the following system of linear equations. x + y + z = α, x + βy + z = γ, x + y + αz = β. If this system has at least one solution, then which of the following statements is (are) true? a)If α = 1 then γ = 1 b)If β = 1 then γ = α c)If β  ≠ 1 then α = 1 d)If γ = 1 then? has been provided alongside types of Suppose  Consider the following system of linear equations. x + y + z = α, x + βy + z = γ, x + y + αz = β. If this system has at least one solution, then which of the following statements is (are) true? a)If α = 1 then γ = 1 b)If β = 1 then γ = α c)If β  ≠ 1 then α = 1 d)If γ = 1 then? theory, EduRev gives you an ample number of questions to practice Suppose  Consider the following system of linear equations. x + y + z = α, x + βy + z = γ, x + y + αz = β. If this system has at least one solution, then which of the following statements is (are) true? a)If α = 1 then γ = 1 b)If β = 1 then γ = α c)If β  ≠ 1 then α = 1 d)If γ = 1 then? tests, examples and also practice UPSC tests.
Explore Courses for UPSC exam

Top Courses for UPSC

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev