On the existence of matrices with constrained elements,rows and columns

Let the following be given: two n × m real matrices, E and F, such that F ? E, three real n-rows, p, a and b, such that b ? a, and three real m-columns, t, c and d, such that d ? c. We give inequalities relating the given matrices and vectors, equivalent to the consistency of the system

$\text{F ? X ? E}$

,

$\text{d ? Xt ? c}$

,

$\text{b ? pX ?a}$

, where X is an n × m unknown real matrix.