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

  1. Classify a 2x2 system so the geometry of simultaneous equations is clear.
  2. Use row operations and Gaussian elimination to solve 3x3 systems step by step.
  3. 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