▦ Matrices & Vectors

7 calculators in this category.

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Add, multiply and raise matrices to powers, find the inverse and determinant, and row-reduce to echelon form with every row operation listed.

Get eigenvalues and eigenvectors, the null space and rank, and the cross and dot products of vectors — with exact fractions instead of rounded decimals.

Matrix Calculator

Add, subtract and multiply matrices, multiply by a scalar, transpose, invert and raise to powers — with exact fractions, the determinant, rank and trace.

Inverse Matrix

Find the inverse of a square matrix with exact fractions — determinant, cofactor matrix, adjugate and Gauss–Jordan steps — or see why it is singular.

Determinant

Find the determinant of a 2×2, 3×3 or larger matrix exactly, with cofactor expansion steps, the rule of Sarrus and what the value means.

Eigenvalue

Find the eigenvalues and eigenvectors of a 2×2 to 5×5 matrix — characteristic polynomial, exact values where possible, complex eigenvalues and checks.

Cross Product

Find the cross product a × b of two 3D vectors with steps, plus the dot product, magnitudes, angle, unit normal, parallelogram area and triple product.

Null Space

Find a basis for the null space (kernel) of a matrix — the solutions of Ax = 0 — with the RREF, pivot and free variables, rank and nullity.

Row Echelon Form

Reduce a matrix to row echelon form (REF) and reduced row echelon form (RREF) with every row operation, exact fractions, rank and pivots — and solve augmented systems.

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