Solution of equations
Equations, Matrices & Numerical Methods
Linear systems, row operations, residual checks, pivoting, and engineering examples. The aim is not just to get answers, but to see why a method is stable enough to trust.
A sensible order through these tools
- Classify a 2x2 system so the geometry of simultaneous equations is clear.
- Use row operations and Gaussian elimination to solve 3x3 systems step by step.
- Check the computed answer with a residual before treating it as an engineering result.
Equations & matrices
Linear systems
Start with simultaneous equations, then move into row reduction and solution checks.
Equations & matrices
Matrix methods
Practise the row operations that make elimination work.
Equations & matrices
Solution checks
Use residuals to check whether an approximate solution actually fits the original equations.
Equations & matrices
Numerical stability
Watch pivot choice and rounding before trusting decimal row reduction.
Equations & matrices
Circuit systems
Turn circuit-style equations into a matrix system and solve the currents.
Next build layer
Coming from the v9 pack
Gauss-Jordan
matrix products
determinants
inverse matrices
Cramer's rule
Jacobi iteration
Gauss-Seidel
bisection
Newton-Raphson
synthetic division
polynomial roots