Matrix Inversion Method Calculator
Solve systems of linear equations using matrix inversion with detailed step-by-step calculations including determinant, cofactor, and adjugate matrices.
Matrix Inversion Method Calculator
Solve systems of linear equations using matrix inversion: X = A⁻¹B
Enter equations above and click solve to see the solution
What is Matrix Inversion Method?
Matrix Inversion Method solves systems of linear equations by finding the inverse of the coefficient matrix and multiplying it with the constants vector.
Formula:
For system AX = B
where A⁻¹ is the inverse of matrix A
Steps to find matrix inverse:
- Calculate the determinant of the coefficient matrix
- Find the matrix of minors
- Apply the checkerboard pattern of signs (cofactor matrix)
- Transpose the cofactor matrix (adjugate matrix)
- Divide by the determinant to get the inverse
- Multiply the inverse by the constants vector
Conditions:
- The coefficient matrix must be square (n × n)
- The determinant must be non-zero (matrix must be invertible)
- Most practical for small systems (2×2 or 3×3)
Advantages:
- Direct method - no iterative steps
- Useful when solving multiple systems with same coefficient matrix
- Provides insight into matrix properties
Disadvantages:
- Computationally expensive for large matrices
- Cannot be used if determinant is zero
- Numerical errors can accumulate in calculations