
Linear Combination Explorer (click image
at left to view)
 Starts with an assortment of examples of linear combinations; press [PageDown] to scroll through them. Rational numbers can be entered as coefficients; use [Space] to cycle through the coefficients and [C] to clear all coefficients to 0.
 On the last page, pressing [V] and [S] display labels indicating the notation used for vectors and scalars, respectively.
 [Home] restarts the examples with "linear combination problems" of building some vector as a linear combination of the given collection. Press the [Up] and [Down] arrows to change targets: some are possible to build (i.e., give consistent systems) and some are impossible (i.e., give inconsistent systems); most examples are linearly dependent and allow multiple solutions when consistent, so that this concept can be explored. To show the solution (or best approximation), press [?].
