Home
Back
Linear Equation System Solution:
| From: | To: |
A system of linear equations is a collection of one or more linear equations involving the same set of variables. The solution is the set of values that satisfies all equations simultaneously.
The calculator uses matrix inversion to solve the system:
Where:
Explanation: The calculator finds the inverse of the coefficient matrix and multiplies it by the constants vector to obtain the solution.
Details: Linear equation systems are fundamental in mathematics, engineering, physics, economics, and many other fields. They are used to model and solve real-world problems involving multiple variables and constraints.
Tips: Enter the coefficient matrix with rows separated by newlines and elements separated by spaces. Enter the constants vector with values separated by spaces. The matrix must be square and invertible.
Q1: What if the matrix is not invertible?
A: If the matrix is singular (determinant = 0), the system may have no solution or infinitely many solutions. The calculator will indicate if the matrix is not invertible.
Q2: Are there other methods to solve linear systems?
A: Yes, other methods include Gaussian elimination, LU decomposition, and iterative methods. Matrix inversion is one of the direct methods.
Q3: What are the limitations of this method?
A: Matrix inversion can be computationally expensive for large matrices and may suffer from numerical instability. For large systems, other methods are preferred.
Q4: Can I solve non-square systems?
A: This calculator only solves square systems (number of equations = number of variables). Non-square systems require different approaches.
Q5: What precision can I expect?
A: The calculator uses floating-point arithmetic, so results may have limited precision due to rounding errors, especially for ill-conditioned matrices.