  Given an $a$-dimensional linear subspace $\mathfrak{A}$ in $\mathbb{R}^d$
which contains a badly approximable $b$-dimensional subspace $\mathfrak{B}
\subset \mathfrak{A}$. We study the badly approximability almost all
$c$-dimensional linear subspaces $\mathfrak{C} \subset \mathfrak{A}$.
