linear algebra Calculators

2x2 Matrix Determinant Calculator

Calculate the determinant of a 2x2 matrix

Calculate the dot product of two vectors in 3D space

Calculate the magnitude (length) of a vector

Calculate the trace (sum of diagonal elements) of a 3x3 matrix

Calculate the angle between two 2D vectors

Solve a system of two linear equations with two variables

Calculate the scalar projection of one vector onto another

Multiply a 2x2 matrix by a scalar value

Calculate the Euclidean distance between two points in 3D space

Calculate the cross product magnitude of two 2D vectors

Calculate the determinant of square matrices up to 4x4 with step-by-step solutions

Calculate dot product, magnitude, and angle between two vectors in 2D or 3D space

Find eigenvalues and eigenvectors of 2x2 matrices with detailed solutions

Calculate the inverse of a 2x2 matrix with determinant check and step-by-step solution

Calculate cross product of two 3D vectors including magnitude and direction

Solve systems of two linear equations using Cramer's rule with solution verification

Calculate the rank of matrices using row reduction and Gaussian elimination

Analyze quadratic forms, determine definiteness, and find canonical form

Convert linearly independent vectors into orthonormal basis using Gram-Schmidt process

Find transformation matrices for rotations, reflections, scaling, and shearing