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A system of linear equations AX = B is said to be inconsistent, if the system of equations has
- a)Trivial Solution
- b)Infinite Solutions
- c)No Solution
- d)Unique Solutions
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A system of linear equations AX = B is said to be inconsistent, if the...
A linear system is said to be consistent if it has at least one solution; and is said to be inconsistent if it has no solution. have no solution, a unique solution, and infinitely many solutions, respectively.
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A system of linear equations AX = B is said to be inconsistent, if the...
if AX=B then X=A^-1B If |A|=0 i.e no solution then the system of ilinear eq. is inconsistent
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A system of linear equations AX = B is said to be inconsistent, if the...
In a system of linear equations, AX = B, where A is a matrix of coefficients, X is a matrix of variables, and B is a matrix of constants, the system is said to be inconsistent if it has no solution.
Explanation:
1. Consistent System: A system of linear equations is said to be consistent if it has at least one solution. This means that there exists a set of values for the variables that satisfies all the equations in the system.
2. Inconsistent System: On the other hand, a system of linear equations is said to be inconsistent if it has no solution. This means that there are no values for the variables that satisfy all the equations in the system simultaneously.
3. Trivial Solution: A system of linear equations can have a unique solution, which is called a trivial solution. In this case, there is only one set of values for the variables that satisfies all the equations in the system. This occurs when the system has as many equations as variables and the determinant of the coefficient matrix, A, is non-zero.
4. Infinite Solutions: A system of linear equations can also have infinitely many solutions. In this case, there are infinitely many sets of values for the variables that satisfy all the equations in the system. This occurs when the system has more variables than equations and the determinant of the coefficient matrix, A, is zero.
5. No Solution: However, when a system of linear equations is inconsistent, it means that there are no values for the variables that satisfy all the equations in the system. This occurs when the system has more equations than variables and the determinant of the coefficient matrix, A, is zero.
6. Determinant Test: The determinant of the coefficient matrix, A, is a useful tool to determine the consistency of a system of linear equations. If the determinant is non-zero, the system is consistent and has a unique solution. If the determinant is zero, the system may have either infinitely many solutions or no solutions, depending on the number of equations and variables.
Therefore, in the given options, option 'C' - No Solution, correctly represents an inconsistent system of linear equations.
Explanation:
1. Consistent System: A system of linear equations is said to be consistent if it has at least one solution. This means that there exists a set of values for the variables that satisfies all the equations in the system.
2. Inconsistent System: On the other hand, a system of linear equations is said to be inconsistent if it has no solution. This means that there are no values for the variables that satisfy all the equations in the system simultaneously.
3. Trivial Solution: A system of linear equations can have a unique solution, which is called a trivial solution. In this case, there is only one set of values for the variables that satisfies all the equations in the system. This occurs when the system has as many equations as variables and the determinant of the coefficient matrix, A, is non-zero.
4. Infinite Solutions: A system of linear equations can also have infinitely many solutions. In this case, there are infinitely many sets of values for the variables that satisfy all the equations in the system. This occurs when the system has more variables than equations and the determinant of the coefficient matrix, A, is zero.
5. No Solution: However, when a system of linear equations is inconsistent, it means that there are no values for the variables that satisfy all the equations in the system. This occurs when the system has more equations than variables and the determinant of the coefficient matrix, A, is zero.
6. Determinant Test: The determinant of the coefficient matrix, A, is a useful tool to determine the consistency of a system of linear equations. If the determinant is non-zero, the system is consistent and has a unique solution. If the determinant is zero, the system may have either infinitely many solutions or no solutions, depending on the number of equations and variables.
Therefore, in the given options, option 'C' - No Solution, correctly represents an inconsistent system of linear equations.
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A system of linear equations AX = B is said to be inconsistent, if the system of equations hasa)Trivial Solutionb)Infinite Solutionsc)No Solutiond)Unique SolutionsCorrect answer is option 'C'. Can you explain this answer?
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