Matrix Calculators
Inverse Matrix Calculator: Gauss–Jordan and Adjugate Method
Find the inverse of a matrix by Gauss–Jordan elimination or the adjugate method with a detailed solution and a check; the answer in fractions.
Determinant Calculator: Gaussian Elimination and Cofactor Expansion
Find the determinant of a matrix up to 6×6 by Gaussian elimination or cofactor expansion, with the rule of Sarrus for 3×3 and a detailed solution.
Matrix Operations Calculator: Addition, Multiplication, Transpose
Matrix calculator: addition and subtraction, scalar and matrix multiplication, transpose and matrix powers with a step-by-step solution in fractions.
Matrix Rank Calculator by Gaussian Elimination
Find the rank of a matrix up to 6×6: reduction to row echelon form by Gaussian elimination with a detailed solution and pivot columns.
Consistency of a Linear System Calculator: Rouché–Capelli
The consistency of a system of linear equations by ranks and its general solution, by the Rouché–Capelli theorem.
Eigenvalue and Eigenvector Calculator with Steps
Eigenvalues and eigenvectors of a matrix through the characteristic polynomial, step by step.
Matrix Minor and Cofactor Calculator
The minor and cofactor of a chosen element of a square matrix, with the solution.
System of Linear Equations Solver: Cramer, Gauss, Inverse Matrix
The calculator solves systems of 2 and 3 linear equations by Cramer's rule, Gaussian elimination and the inverse matrix method with exact fractions.
Matrix calculators perform the main operations of linear algebra with step-by-step solutions: matrix addition and multiplication, transpose, determinant, inverse and rank. Entries can be fractions — every calculation is exact, and each step of Gaussian elimination is shown.
- Matrix operations — sum, difference, scalar and matrix multiplication, transpose, powers.
- Determinant — by Gaussian elimination or cofactor expansion, up to 6×6.
- Inverse matrix — by Gauss–Jordan elimination or the adjugate method.
- Matrix rank — by reduction to row echelon form.