Linear Algebra
Class 12

Cramer's Rule

x=det(Ax)det(A),y=det(Ay)det(A)x = \frac{\det(A_x)}{\det(A)}, \quad y = \frac{\det(A_y)}{\det(A)}
0510150246810
x = det(Aₓ)/det(A), y = det(Aᵧ)/det(A)

Adjust Variables

det(A)
detA =
0.110

Solves linear equations using determinants. Replace column with constants to get numerator determinant.

Real-World Applications

Circuit analysis — Solving for currents in mesh analysis.

Economics — Equilibrium prices in simultaneous equations.

Structural engineering — Force distribution calculations.

Chemical equilibrium — Concentration calculations.

Transportation — Traffic flow optimization.

Supply chain — Inventory optimization.

Finance — Portfolio optimization constraints.

Robotics — Inverse kinematics solutions.

Physics — Coupled oscillator equations.

Environmental — Pollutant dispersion modeling.

Community Explanations

No community explanations yet. Be the first to share yours!

to write your own explanation

Community Aha! Moments

to share your insights

No insights yet. Be the first to share!

Related Formulas