Math
Solving systems with matrices.
Definition
Using matrix operations to solve systems of linear equations. The system is written in matrix form Ax = b, and solutions can be found using inverse matrices (x = A⁻¹b), row reduction (Gaussian elimination), or Cramer's rule with determinants.
How it works · 4 phases
Step by step.
- Write the system of equations as an augmented matrix [A|b].
- Use row operations to reduce to row echelon or reduced row echelon form.
- Back-substitute to find each variable.
- Alternatively, compute A⁻¹ and multiply by b to get x = A⁻¹b.
Examples
Real-world.
- 1 Solving 2x + y = 5, x − y = 1 using an augmented matrix and row reduction
- 2 Using a graphing calculator's matrix function to solve a 3×3 system