Question
What characteristics make a problem solvable by a system of linear equations
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GPT 3.5
1. Linearity: The problem must involve linear relationships between the variables. This means that the variables appear to the first power only, with no exponents or other non-linear terms.
2. Consistency: The problem must have a solution that satisfies all of the equations simultaneously. In other words, the equations must not contradict each other.
3. Independence: The equations in the system must not be redundant or dependent on each other. Each equation should provide new information or constraints on the problem.
4. Number of equations: The number of equations in the system should be equal to or greater than the number of variables in order to have a unique solution.
5. Non-singularity: The system's coefficient matrix must be non-singular, meaning it has a non-zero determinant. This ensures that the equations are independent and can be solved using standard methods like Gaussian elimination or matrix inversion.
6. Well-posedness: The problem must be well-defined and have a single, unique solution. There should be no ambiguity or multiple possible solutions.
2. Consistency: The problem must have a solution that satisfies all of the equations simultaneously. In other words, the equations must not contradict each other.
3. Independence: The equations in the system must not be redundant or dependent on each other. Each equation should provide new information or constraints on the problem.
4. Number of equations: The number of equations in the system should be equal to or greater than the number of variables in order to have a unique solution.
5. Non-singularity: The system's coefficient matrix must be non-singular, meaning it has a non-zero determinant. This ensures that the equations are independent and can be solved using standard methods like Gaussian elimination or matrix inversion.
6. Well-posedness: The problem must be well-defined and have a single, unique solution. There should be no ambiguity or multiple possible solutions.
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