선형 대수학 계산기

Add subtract and multiply 2D and 3D vectors. See formula, step-by-step solution and all rearrangements. Instant math solver.

Multiply matrices of any compatible dimensions. See formula, step-by-step solution and all rearrangements. Instant math solver.

Transpose any matrix and check symmetry. See formula, step-by-step solution and all rearrangements. Instant math solver.

Calculate the rank of any matrix using row echelon reduction. Enter matrix entries — see rank, nullity, pivot positions, and row operations. Free.

Calculate the null space (kernel) of any matrix. Enter your matrix — see the null space basis vectors with row reduction steps. Free.

Solve 2×2 and 3×3 systems of linear equations. Enter your coefficients — see the solution with Gaussian elimination or Cramer's rule steps. Free.

Orthogonalize a set of vectors using Gram-Schmidt process. Enter your vectors — see each orthonormal basis vector with projection steps. Free.

3D cross product and orthogonal vector. Step-by-step solution with matrix visualization and formula. Instant linear algebra solver.

Calculate the dot product of two vectors. Enter vector components — see the scalar result, angle between vectors, and projection. Free.

Calculate the magnitude of any 2D or 3D vector. Enter vector components — see |v| with the distance formula and unit vector. Free.