System of Equations Solver - Solve Linear Equations in Matrix Form
Solve systems of linear equations using matrix form (Ax=b) online. Enter your coefficient matrix A and constant vector b to find the solution vector x. Visualize the equations and their intersection point.
Input Equations
Enter the coefficient matrix A and the constant vector b for the system of equations in the form Ax = b.
Enter matrix as a 2D array in JSON format.
Enter vector as a 1D array in JSON format.
Solution Vector (x)
Visualization
The plot below visualizes the system of equations. Each equation represents a line, and the solution vector x is the intersection point of these lines.
Understanding System of Equations (Ax=b)
A system of linear equations can be represented in matrix form as Ax = b, where A is the coefficient matrix, x is the vector of variables, and b is the constant vector. Solving this system means finding the values of x that satisfy all equations simultaneously. For a system of two linear equations, each equation represents a line on a 2D graph. The solution to the system is the point where these lines intersect. This tool uses matrix algebra to efficiently solve such systems and visualizes the equations and their solution point, making it easier to understand linear algebra concepts and verify solutions graphically.
- Coefficient Matrix (A): Contains the coefficients of the variables in each equation.
- Variable Vector (x): The vector of unknowns we are solving for.
- Constant Vector (b): Contains the constant terms of each equation.
- Solution Vector (x): The calculated values of the variables that satisfy the system.