# Linear Algebra

Linear Algebra is a branch of mathematics which explores the concepts of vector spaces.  Linear algebra also defines linear mappings between vector spaces and the properties common amongst all vector spaces.
Linear algebra also includes the theory of systems of linear equations, matrices, determinants, and linear transformations .

vCalc's Linear Algebra library consists of linear equations and calculators.

## Linear Algebra Equations

• Characteristic Polynomial of a 2x2 Matrix
• Characteristic Polynomial of a 3x3 Matrix
• Cramer's Rule (three equations)
• Cramer's Rule (three equations, solved for x)
• Cramer's Rule (three equations, solved for y)
• Cramer's Rule (three equations, solved for z)
• Cramer's Rule (two equations)
• Cramer's Rule (two equations, solved for x)
• Cramer's Rule (two equations, solved for y)
• Determinant of 3-by-3 Matrix
• Determinant of a 2-by-2 Matrix
• Determinant of a 2x2 Matrix
• Eigenvalues of a 2x2 Matrix
• Least Squares (n=3)
• Least Squares (n=4)
• Minor of a 3x3 Matrix
• Multiplication of a 2x2 Matrix by a 2x1 Matrix
• Multiplication of a 2x2 Matrix by a Scalar
• Multiplication of a 2x3 Matrix and a 3x2 Matrix
• Multiplication of a 3x3 Matrix and a 3x1 Matrix
• Row Echelon Form of a 3x3 Matrix
• row echelon test
• Trace of a 2x2 Matrix
• Trace of a 3x3 Matrix