Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Consider the following system of equations in...
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Consider the following system of equations in three real variables x, y, z.
2x – 3y + 7z = 5
3x + y – 3z = 13
2x + 19y – 47z = 32
The system of equation has
- a)No solution
- b)A unique solution
- c)More than one but a finite number of solutions
- d)An infinite number of solutions
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Consider the following system of equations in three real variables x, ...
Augmented matrix will be
Rank of A ≠ Rank of Augmented matrix
Hence given system of equations has no solution.
Most Upvoted Answer
Consider the following system of equations in three real variables x, ...
Understanding the System of Equations
The system of equations given is:
1. 2x - 3y + 7z = 5
2. 3x + y - 3z = 13
3. 2x + 19y - 47z = 32
We need to analyze these equations to determine the nature of their solutions.
Form the Augmented Matrix
To investigate the solutions, we can represent the system as an augmented matrix:
| 2 -3 7 | 5 |
| 3 1 -3 | 13 |
| 2 19 -47 | 32 |
Row Reduction
By applying Gaussian elimination, we can simplify the augmented matrix to identify any contradictions or dependencies among the equations.
1. Start with the first row and use it to eliminate variables from the second and third rows.
2. After performing row operations, look for discrepancies, such as a row that leads to a false statement (e.g., 0 = c where c is a non-zero constant).
Identifying No Solutions
During the row reduction process, if we find a row resulting in a contradiction (like 0 = 7), it indicates that the system has no solution.
Conclusion
After performing the necessary operations, it becomes evident that:
- There is a contradiction in the system.
- Hence, the correct answer is option 'A': No solution.
This conclusion highlights that the equations represent planes in three-dimensional space that do not intersect at any point.
The system of equations given is:
1. 2x - 3y + 7z = 5
2. 3x + y - 3z = 13
3. 2x + 19y - 47z = 32
We need to analyze these equations to determine the nature of their solutions.
Form the Augmented Matrix
To investigate the solutions, we can represent the system as an augmented matrix:
| 2 -3 7 | 5 |
| 3 1 -3 | 13 |
| 2 19 -47 | 32 |
Row Reduction
By applying Gaussian elimination, we can simplify the augmented matrix to identify any contradictions or dependencies among the equations.
1. Start with the first row and use it to eliminate variables from the second and third rows.
2. After performing row operations, look for discrepancies, such as a row that leads to a false statement (e.g., 0 = c where c is a non-zero constant).
Identifying No Solutions
During the row reduction process, if we find a row resulting in a contradiction (like 0 = 7), it indicates that the system has no solution.
Conclusion
After performing the necessary operations, it becomes evident that:
- There is a contradiction in the system.
- Hence, the correct answer is option 'A': No solution.
This conclusion highlights that the equations represent planes in three-dimensional space that do not intersect at any point.
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Consider the following system of equations in three real variables x, y, z.2x – 3y + 7z = 53x + y – 3z = 132x + 19y – 47z = 32The system of equation hasa)No solutionb)A unique solutionc)More than one but a finite number of solutions d)An infinite number of solutionsCorrect answer is option 'A'. Can you explain this answer?
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Consider the following system of equations in three real variables x, y, z.2x – 3y + 7z = 53x + y – 3z = 132x + 19y – 47z = 32The system of equation hasa)No solutionb)A unique solutionc)More than one but a finite number of solutions d)An infinite number of solutionsCorrect answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider the following system of equations in three real variables x, y, z.2x – 3y + 7z = 53x + y – 3z = 132x + 19y – 47z = 32The system of equation hasa)No solutionb)A unique solutionc)More than one but a finite number of solutions d)An infinite number of solutionsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following system of equations in three real variables x, y, z.2x – 3y + 7z = 53x + y – 3z = 132x + 19y – 47z = 32The system of equation hasa)No solutionb)A unique solutionc)More than one but a finite number of solutions d)An infinite number of solutionsCorrect answer is option 'A'. Can you explain this answer?.
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