Choose a <basis> for the first subspace of a <flag>, extend it to a <basis> for the second, and continue until obtaining a <basis> of the whole <vector space>. Do the same for the target <flag>. The unique <linear map> sending the first adapted <basis> to the second is invertible and sends every flagged subspace to its counterpart. Hence the action is \b[<transitive group action>[transitive]].

Solution

Past exam of the Probability, statistics and options II course of the University of Oxford / 2008 / A / 2 / b / i / Solution

 Solution (source code)