Lesson 3 of 10Article20 min
Linear Systems & Gaussian Elimination
Row reduce the augmented matrix [A|b] to echelon or reduced echelon form. Pivot positions reveal whether solutions exist and how many free variables remain.
Solving Ax = b
Row reduce the augmented matrix [A|b] to echelon or reduced echelon form. Pivot positions reveal whether solutions exist and how many free variables remain.
- Consistent: at least one solution; inconsistent: none.
- Unique solution: pivot in every variable column.
- Infinite solutions: free variables → parametric form.
- Elementary ops: swap rows, scale row, add multiple of one row to another.
Write the solution set clearly: particular solution + span of null-space basis vectors.