  We study the evolution of random matroids represented by the sequence of
random matrices over ${\mathbb F}_q$ where columns are added one after the
other, and each column vector is a uniformly random vector in ${\mathbb
F}_q^n$, independent of each other. We study the appearance of matroid minors,
the appearance of circuits, the evolution of the connectivities and the
critical number. We settle several open problems in the literature.
