Visualising the span of two vectorsThis applet visualises the span of two vectors in R3 using linear combinations.
Vector equations of lines in R2This applet shows a line in R2 and the vector form of its equation.
Vector equations of planes in R3This applet shows a plane in R3 and the vector form of its equation.
Vector equations of lines in R3This applet shows a line in R3 and the vector form of its equation.
Visualising row addition on a 3×3 matrixThis applet shows how the determinant is unaffected by the elementary row operation of addition of a scalar multiple of a row to another row.
Visualising row addition on a 2×2 matrixThis applet shows how the determinant is unaffected by the elementary row operation of addition of a scalar multiple of a row to another row.
Visualising row, column and solution spacesThis applet shows the row, column, and solution spaces of a 3x3 matrix M.
Columns of a matrix and the rank-nullity theoremThis applet shows how the column space, solution space, rank and nullity of a matrix M change as you append additional columns. Initially the matrix M has a single column. You can add extra columns to M by editing the text boxes on the right of the applet, and clicking the ‘Append column’ button. The […]
Linear transformations and eigenvectorsThis applet illustrates the effect of a linear transformation in R2 on the unit circle/unit disk, and the geometric meaning of eigenvectors, eigenvalues and determinant.
Vector projectionsThis applet aims to demonstrate visually the projection of a vector u onto a vector v.