Let $T$ be an injective linear transformation from ${\mathbb R}^r$ to ${\mathbb R}^s$. Let $A$ be the matrix associated to $T$ and let $B$ be the row-echelon reduction of $A$.

 1. Determine which of the following conditions can hold:

A. $r=7, s=5$ and $B$ has 4 pivots.
B. $r=5, s=7$ and $B$ has 5 pivots.
C. $r=5, s=7$ and $B$ has 4 pivots.
D. $r=7, s=5$ and $B$ has 5 pivots.
E. None of the above.