Linear Algebra
Solving Systems of Linear Equations
1. Solving a system of linear equations
- Find a particular solution to
Ax = b.- Build the augmented matrix in the form of
[A|b]. - Elementary transformation: transform the matrix to the row-echelon form (REF).
- Build the augmented matrix in the form of
- Find all solutions to
Ax = 0.- Gaussian elimination: transformed the matrix A to the reduced REF.
- or Minus-1 Trick: adding rows at the places where the pivots on the diagonal are missing.
- Derive all solutions for
Ax = 0.
- Combine the solutions from steps 1 and 2 to the general solution.