© 2000−2013  P. BogackiLinear Algebra Toolkit - Main Pagev. 1.24 

This Linear Algebra Toolkit is composed of the modules listed below. Each module is designed to help a linear algebra student learn and practice a basic linear algebra procedure, such as Gauss-Jordan reduction, calculating the determinant, or checking for linear independence.

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 MODULES

Systems of linear equations and matrices
Row operation calculatorInteractively perform a sequence of elementary row operations on the given m x n matrix A.
Transforming a matrix to row echelon formFind a matrix in row echelon form that is row equivalent to the given m x n matrix A.
Transforming a matrix to reduced row echelon formFind the matrix in reduced row echelon form that is row equivalent to the given m x n matrix A.
Solving a system of linear equationsSolve the given system of m linear equations in n unknowns.
Calculating the inverse using row operationsFind (if possible) the inverse of the given n x n matrix A.
Determinants
Calculating the determinant using row operationsCalculate the determinant of the given n x n matrix A.
Vector spaces
Linear independence and dependenceGiven the set S = {v1, v2, ... , vn} of vectors in the vector space V, determine whether S is linearly independent or linearly dependent.
Determining if the set spans the spaceGiven the set S = {v1, v2, ... , vn} of vectors in the vector space V, determine whether S spans V.
Finding a basis of the space spanned by the setGiven the set S = {v1, v2, ... , vn} of vectors in the vector space V, find a basis for span S.
Finding a basis of the null space of a matrixFind a basis of the null space of the given m x n matrix A. (Also discussed: rank and nullity of A.)
Linear transformations
Finding the kernel of the linear transformationFind the kernel of the linear transformation L: V→W. (Also discussed: nullity of L; is L one-to-one?)
Finding the range of the linear transformationFind the range of the linear transformation L: V→W. (Also discussed: rank of L; is L onto W?)

 ADDITIONAL INFO