Calculators for Linear Algebra

Linear Algebra tells about linear equations. A linear equation is e.g. 2x-3y+4z=8. This has several unknowns, x, y and z, which can only be solved with more independant equations of the same kind. Linear equations are frequently used in mathematics, like in mathematical economics to describe economic relations. Linear algebra offers comfortable methods for their calculations. Here you will find calculators for matrices, determinants, equation systems and for vectors in ℜ³.

A linear equation with two unknowns describes a line in a plane on which the solutions of this equation lie. Therefore the equation is called linear. With three unknowns, like the equation in the example above, the solutions form a plane in space. With more unknowns, we are running out of visualization options in our three-dimensional world, but mathematics has no problems with this.

A matrix, multiple matrices are two-dimensional arrays with values arranged in rows and columns. One linear equation can be accommodated per line. Here you can calculate with one or two matrices, the result is displayed in a new matrix.
Determinants indicate whether systems of linear equations in a matrix are solvable or not. If the result is not 0, then the system of equations can be clearly solved.
Like matrices, equation systems contain linear equations, but whose solutions are given in a separate column. They can be used to solve x independent linear equations with x unknowns.
A vector is a directed line in space, a one-dimensional matrix. For example, forces are often represented as vectors.
The results of the three calculators for the matrices, determinants and systems of equations can be moved to the other calculators in order to continue calculating there.