Linear algebra

Matrices, determinants and vectors.

• Determinant Calculator

  This determinant calculator finds the determinant of a 2×2, 3×3 or 4×4 matrix exactly. It shows the cofactor expansion step by step and checks the answer a second way, by row reduction.

• Inverse Matrix Calculator

  This inverse matrix calculator finds the inverse of a 2×2, 3×3 or 4×4 matrix with exact fractions. It shows the ad − bc formula for 2×2 matrices and every Gauss–Jordan row operation for larger ones, then checks that A × A⁻¹ is the identity matrix.

• Unit Tangent Vector Calculator

  This unit tangent vector calculator finds T(t) = r′(t)/|r′(t)| for a curve r(t) = ⟨x(t), y(t), z(t)⟩ whose components are polynomials in t. It differentiates each component, finds the length of r′(t), and gives T at the value of t you choose exactly — for example ⟨1/3, 2/3, 2/3⟩ — with decimals when roots appear.

• Unit Vector Calculator

  This unit vector calculator divides a vector by its magnitude to give the unit vector in the same direction — for example ⟨3, 4⟩ becomes ⟨3/5, 4/5⟩. It works for 2D, 3D and 4D vectors, keeps answers exact (with simplified square roots), and checks that the result has length 1.

• Vector Calculator: Unit Normal, Resultant and Orthogonal Vectors

  This vector calculator finds the unit normal vector N(t) of a curve at a point, the normal vector to two vectors (the cross product), the resultant of two vectors, and whether two vectors are orthogonal. Answers are exact, with simplified square roots, and each one is checked.