Linear algebra just got more manageable. This collection brings together the RREF Matrix Calculator, 3×3 Matrix Inverse Calculator, and Dot Product Calculator for everyday coursework, alongside the QR Factorization Calculator and System of Equations Calculator for deeper problem-solving.
Browse the most-popular list or open the Trending tab to see what students and engineers are reaching for. Everything is free, requires no account, and runs on any device.
- Fraction Calculator
- Matrix Calculator
- Slope Calculator
- Algebra Calculator
- Trigonometry Calculator
- Percentage Calculator
- Probability Calculator
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System of Equations CalculatorSolve a 2-variable linear system a₁x+b₁y=c₁, a₂x+b₂y=c₂ instantly using Cramer's rule. Detects parallel/identical lines with no unique solution.
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3×3 System of Equations CalculatorSolve a 3×3 system of linear equations in x, y, z using Cramer's rule. Enter all 12 coefficients and get the exact solution and determinant instantly.
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3x3 System of Equations CalculatorSolve a 3x3 system of linear equations using Cramer's Rule. Enter coefficients to find x, y, z plus all determinants instantly.
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Linear System of 3 Unknowns SolverSolve a system of 3 linear equations in 3 unknowns (x, y, z) by Gauss-Jordan elimination. Shows the unique solution and the reduced row echelon form.
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Reduced Row Echelon Form (RREF) CalculatorFree RREF calculator. Reduce any matrix (up to 6x6) to reduced row echelon form using Gauss-Jordan elimination and find the matrix rank instantly.
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3D Vector Cross Product CalculatorCompute the cross product of two 3D vectors a × b instantly. Get each component (x, y, z) plus the magnitude of the resulting perpendicular vector.
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Matrix Determinant CalculatorFree matrix determinant calculator for 2×2 and 3×3 matrices. Enter your matrix entries to instantly compute det A via cofactor expansion.
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2×2 Matrix Determinant CalculatorCompute the determinant of a 2×2 matrix instantly using det = ad − bc. Enter the four entries a, b, c, d and get the result with steps.
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2×2 Eigenvector CalculatorFind the eigenvalues and eigenvectors of any 2×2 matrix instantly. Enter a, b, c, d and get λ₁, λ₂ and their eigenvectors with full working.
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2x2 Eigenvalue CalculatorFind the eigenvalues of any 2x2 matrix instantly. Computes real or complex conjugate eigenvalues from the trace and determinant using the characteristic equation.
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Characteristic Polynomial CalculatorFind the characteristic polynomial of a 2×2 or 3×3 matrix. Computes coefficients, trace and determinant from det(A − λI) instantly.
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Cosine Similarity CalculatorCalculate cosine similarity between two vectors, plus their dot product, magnitudes, and the angle between them in degrees and radians.
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2x2 Eigenvalue CalculatorFind the eigenvalues of any 2x2 matrix instantly. Computes trace, determinant, discriminant, and real or complex eigenvalues with full steps.
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N-by-N System of Linear Equations Solver (LU Decomposition)Solve a system of n linear equations in n unknowns A·x = b. Uses LU decomposition with partial pivoting for the unique solution vector x and determinant.
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Matrix Rank CalculatorCompute the rank of any real matrix A online. Enter your m x n matrix and get the number of linearly independent rows or columns via Gaussian elimination.
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LU Decomposition Calculator with Partial PivotingFree LU decomposition calculator with partial pivoting. Factor a square matrix into L and U with row pivot vector P so that P*A = L*U, plus the determinant.
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Inverse of an n×n Matrix (via LU Decomposition)Compute the inverse of a square n×n matrix online using LU decomposition with partial pivoting. Enter your matrix, get A^-1, determinant and singularity check.
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Euclidean Distance Between Vectors CalculatorCompute the Euclidean (straight-line) distance between two vectors of any dimension using d = sqrt(Σ(aᵢ − bᵢ)²). Fast, free, accurate.
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2x2 Matrix Eigenvalue CalculatorFind the eigenvalues of any 2x2 matrix instantly. Computes real or complex conjugate eigenvalues from the trace and determinant using the characteristic equation.
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Matrix Inverse CalculatorFind the inverse of a 2×2 or 3×3 matrix instantly. Computes the determinant and the inverse A⁻¹ = adj(A)/det(A) with step-by-step results.
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Matrix Transpose CalculatorEnter a matrix as comma-separated values with | for new rows to get its transpose (Aᵀ) instantly. Simple tool for linear algebra and homework.
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Hadamard Product (Element-wise Matrix Product) CalculatorCompute the Hadamard product C = A ∘ B of two equal-size matrices: each entry c_jk = a_jk × b_jk. Element-wise (Schur) multiplication with adjustable display precision.
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Matrix-Vector Product CalculatorCompute the product c = A·x of a matrix A and a column vector x. Enter any rows×cols matrix and a vector; get the resulting column vector instantly.
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QR Factorization CalculatorEnter a matrix (use commas for columns and pipes for rows) to compute its QR factorization and get orthogonal Q and upper-triangular R matrices.
Frequently asked questions
What matrix and linear algebra operations can I find here?
The collection covers matrix inversion (3×3 and n×n via LU decomposition), row reduction to RREF, QR factorization, dot products, matrix transposition, and full system-of-equations solving for both small and larger n-by-n systems. It handles most undergraduate linear algebra coursework in one place.
How accurate are the matrix results?
Calculations use standard numerical algorithms — LU decomposition, Gaussian elimination, and Gram-Schmidt orthogonalization among others — tested against reference solutions. For engineering or safety-critical applications, verify against the governing standard and have a qualified engineer review the work.
Is there a cost to use these calculators?
Every matrix calculator on this site is completely free, with no registration, no subscription, and no time limits. Enter your values, select the operation, and get your result immediately.
Are my matrix entries stored or transmitted?
No. Everything runs in your browser — your matrix data is never sent to our servers, logged, or shared with any third party. Close the tab and all inputs disappear.
Which tools in this collection are the most popular?
The default list is ranked by actual visitor usage, with the most-used tools at the top. Flip to the Trending tab to see what is currently most active, or check Recently Added for the newest tools in the collection.
