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The system of equation kx + y + z = 1,
x + ky + z = k and x = y + kz = k2 has nosolution if k equals
x + ky + z = k and x = y + kz = k2 has nosolution if k equals
- a)0
- b)1
- c)-1
- d)-2
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The system of equation kx + y + z = 1,x + ky + z = k and x = y + kz = ...
⟹ k(k2 − 1) − (k − 1) + (1 − k) = 0
⟹ k(k+1)−1−1] = 0 ⟹ k2 +k−2 = 0
⟹ 1, −2
For k =1, first two equations will become same. ⟹ k = −2
Most Upvoted Answer
The system of equation kx + y + z = 1,x + ky + z = k and x = y + kz = ...
Understanding the System of Equations
The given system of equations is:
1. kx + y + z = 1
2. x + ky + z = k
3. x = y + kz = k²
We want to find the value of k for which this system has no solution.
Condition for No Solution
A system of linear equations has no solution if it is inconsistent. This typically occurs when the equations represent parallel lines or planes that do not intersect.
Analyzing the Equations
- From the third equation, we can express y and z in terms of x:
y = x - kz
z = (k² - x) / k.
- Substituting y and z into the first two equations helps us simplify and analyze the system.
Substituting Values
1. Substitute y and z into the first equation:
kx + (x - kz) + (k² - x) / k = 1.
2. Substitute y and z into the second equation:
x + k(x - kz) + (k² - x) / k = k.
These substitutions can be expanded and simplified to find conditions for k.
Finding the Value of k
Through the simplification process, you will arrive at a situation where the coefficients of x and the constants lead to a contradiction for a specific value of k.
Conclusion
After solving the equations, you will find that k = -2 causes the system to become inconsistent, leading to no solution. Thus, the correct answer is:
- d) -2
The given system of equations is:
1. kx + y + z = 1
2. x + ky + z = k
3. x = y + kz = k²
We want to find the value of k for which this system has no solution.
Condition for No Solution
A system of linear equations has no solution if it is inconsistent. This typically occurs when the equations represent parallel lines or planes that do not intersect.
Analyzing the Equations
- From the third equation, we can express y and z in terms of x:
y = x - kz
z = (k² - x) / k.
- Substituting y and z into the first two equations helps us simplify and analyze the system.
Substituting Values
1. Substitute y and z into the first equation:
kx + (x - kz) + (k² - x) / k = 1.
2. Substitute y and z into the second equation:
x + k(x - kz) + (k² - x) / k = k.
These substitutions can be expanded and simplified to find conditions for k.
Finding the Value of k
Through the simplification process, you will arrive at a situation where the coefficients of x and the constants lead to a contradiction for a specific value of k.
Conclusion
After solving the equations, you will find that k = -2 causes the system to become inconsistent, leading to no solution. Thus, the correct answer is:
- d) -2
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The system of equation kx + y + z = 1,x + ky + z = k and x = y + kz = k2 has nosolution if k equalsa)0b)1c)-1d)-2Correct answer is option 'D'. Can you explain this answer?
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The system of equation kx + y + z = 1,x + ky + z = k and x = y + kz = k2 has nosolution if k equalsa)0b)1c)-1d)-2Correct answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The system of equation kx + y + z = 1,x + ky + z = k and x = y + kz = k2 has nosolution if k equalsa)0b)1c)-1d)-2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The system of equation kx + y + z = 1,x + ky + z = k and x = y + kz = k2 has nosolution if k equalsa)0b)1c)-1d)-2Correct answer is option 'D'. Can you explain this answer?.
The system of equation kx + y + z = 1,x + ky + z = k and x = y + kz = k2 has nosolution if k equalsa)0b)1c)-1d)-2Correct answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The system of equation kx + y + z = 1,x + ky + z = k and x = y + kz = k2 has nosolution if k equalsa)0b)1c)-1d)-2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The system of equation kx + y + z = 1,x + ky + z = k and x = y + kz = k2 has nosolution if k equalsa)0b)1c)-1d)-2Correct answer is option 'D'. Can you explain this answer?.
Solutions for The system of equation kx + y + z = 1,x + ky + z = k and x = y + kz = k2 has nosolution if k equalsa)0b)1c)-1d)-2Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
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