Concise, straightforward explanation of 2D linear transformations. Rotations, reflections, expansions/compressions, and shears are described algebraically and geometrically.

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This module is for users to experiment with fitting a line or parabola to a given data set by means of geometric intuition. Six data sets are given.

The user selects the columns of the \(2 \times 2\) standard matrix for a linear transformation by choosing its columns vectors on a graph of \(\mathbf{R}^2\). The applet provides a wealth of

The user inputs a \(3 \times 3\) transition matrix for a Markov chain along with the initial state of the chain. The user can then simulate steps of the chain one at a time and watch its prog

The user inputs the augmented matrix of a linear system, then has several options for row reducing the matrix to find a solution to the system: the reduction can be done one row operation at a time

This module contains a well-written introduction to numerical solution of systems of linear equations and a Java applet.

The user selects a point \(P\) in \(R^2\) by dragging with the mouse. The coordinates of \(P\) in the standard basis are given along with its coordinates in a second basis, which are calculat

The user selects the entries in a 2 by 2 matrix, which may be any number s between -3 and 3. The matrix is taken to be the standard matrix of a linear transformation. The user may then

The user drags two points in the plane to form the eigenvectors for a transformation; the corresponding eigenvalues are the respective lengths of the vectors. The application shows the standa

The user selects the entries in a 2 by 2 matrix, which may be any numbers between -5 and 5. The matrix is taken to be the standard matrix of a linear transformation.