Let A be an arbitrary upper-triangular n x n matrix and {el, ..., en} be the standard basis of F". Recall one flag for IF" is given by U1 = span{el}, U2 = span{el, e2}, U3 = span {el, e2, e3}, ..., etc., until finally Un = span{el, e2, . .., en) = F. Show that each U; is A-invariant. Intuitively, this means that a matrix is upper triangular with respect to a flag of invariant subspaces