In-class activity: Linear transformations

In-class activity to be completed after an introduction to transformations and ideally in teams. In part 1, students are guided to discover the theorem describing the matrix of a linear transformation from R^n to R^m. In part 2, students learn the one-to-one and onto properties of linear transformations, and are asked to relate these properties to the properties of the matrices (linear independence of columns and columns spanning the codomain).