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Consider the following statements about the given system of equations,
x + 2y + 3z = 0
3x + 4y + 4z = 0
7x + 10y + 12z = 0
x + 2y + 3z = 0
3x + 4y + 4z = 0
7x + 10y + 12z = 0
and choose the correct one
- a)The given system is consistent and has a infinite number of solutions.
- b)The given system is inconsistent.
- c)The data is incomplete.
- d)The given system is consistent and has a unique solution.
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Consider the following statements about the given system of equations,...
Coefficient matrix to the given system of equation is,
Hence, the rank of the coefficient matrix is 3 which is equal to the number of unknown variables in the system.
∴ The system has a unique solution.
∴ The system has a unique solution.
The correct answer is: The given system is consistent and has a unique solution.
Most Upvoted Answer
Consider the following statements about the given system of equations,...
Understanding the System of Equations
The given system of equations is:
1. x + 2y + 3z = 0
2. 3x + 4y + 4z = 0
3. 7x + 10y + 12z = 0
To determine the nature of the solutions, we can analyze these equations using methods like substitution, elimination, or matrix representation.
Matrix Representation
We can represent the system in matrix form as follows:
| 1 2 3 | | x | | 0 |
| 3 4 4 | * | y | = | 0 |
| 7 10 12 | | z | | 0 |
Row Reduction
Using row reduction (Gaussian elimination), we can simplify the augmented matrix to identify the rank and determine if there are unique or infinite solutions.
1. First, perform row operations to simplify:
- R2 = R2 - 3*R1
- R3 = R3 - 7*R1
2. After simplification, if we find that the rank of the coefficient matrix equals the rank of the augmented matrix and equals the number of variables (3), then the system has a unique solution.
Conclusion
In this case, each equation is linearly independent and leads to a unique solution for x, y, and z. Thus, the correct answer is:
Correct Answer: Option D
The system is consistent and has a unique solution. This indicates that there is one specific set of values for x, y, and z that satisfies all three equations simultaneously.
The given system of equations is:
1. x + 2y + 3z = 0
2. 3x + 4y + 4z = 0
3. 7x + 10y + 12z = 0
To determine the nature of the solutions, we can analyze these equations using methods like substitution, elimination, or matrix representation.
Matrix Representation
We can represent the system in matrix form as follows:
| 1 2 3 | | x | | 0 |
| 3 4 4 | * | y | = | 0 |
| 7 10 12 | | z | | 0 |
Row Reduction
Using row reduction (Gaussian elimination), we can simplify the augmented matrix to identify the rank and determine if there are unique or infinite solutions.
1. First, perform row operations to simplify:
- R2 = R2 - 3*R1
- R3 = R3 - 7*R1
2. After simplification, if we find that the rank of the coefficient matrix equals the rank of the augmented matrix and equals the number of variables (3), then the system has a unique solution.
Conclusion
In this case, each equation is linearly independent and leads to a unique solution for x, y, and z. Thus, the correct answer is:
Correct Answer: Option D
The system is consistent and has a unique solution. This indicates that there is one specific set of values for x, y, and z that satisfies all three equations simultaneously.
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Consider the following statements about the given system of equations,x+ 2y+ 3z = 03x+ 4y+ 4z = 07x+ 10y+ 12z = 0and choose the correct onea)The given system is consistent and has a infinite number of solutions.b)The given system is inconsistent.c)The data is incomplete.d)The given system is consistent and has a unique solution.Correct answer is option 'D'. Can you explain this answer?
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Consider the following statements about the given system of equations,x+ 2y+ 3z = 03x+ 4y+ 4z = 07x+ 10y+ 12z = 0and choose the correct onea)The given system is consistent and has a infinite number of solutions.b)The given system is inconsistent.c)The data is incomplete.d)The given system is consistent and has a unique solution.Correct answer is option 'D'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Consider the following statements about the given system of equations,x+ 2y+ 3z = 03x+ 4y+ 4z = 07x+ 10y+ 12z = 0and choose the correct onea)The given system is consistent and has a infinite number of solutions.b)The given system is inconsistent.c)The data is incomplete.d)The given system is consistent and has a unique solution.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements about the given system of equations,x+ 2y+ 3z = 03x+ 4y+ 4z = 07x+ 10y+ 12z = 0and choose the correct onea)The given system is consistent and has a infinite number of solutions.b)The given system is inconsistent.c)The data is incomplete.d)The given system is consistent and has a unique solution.Correct answer is option 'D'. Can you explain this answer?.
Solutions for Consider the following statements about the given system of equations,x+ 2y+ 3z = 03x+ 4y+ 4z = 07x+ 10y+ 12z = 0and choose the correct onea)The given system is consistent and has a infinite number of solutions.b)The given system is inconsistent.c)The data is incomplete.d)The given system is consistent and has a unique solution.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Physics.
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