On the algebraic complexity of a pair of bilinear forms

The problem mentioned in the title is reduced to the evaluation of the range of a set of matrices. The range of matrices $A_1,\dots,A_l$, (denoted by $rg(A_1,\dots,A_l)$,) is the least number of one-dimensional matrices, whose linear combinations represent all $A_i$`s For an operator $A$ in $\mathbb C^n$ there exist a space и and a diagonal operator $B$ with $(A-B)\mathbb C^n\subseteq V$; the minimum of dimensions of such $A_i$`s is denoted by $d(V)$.
Theorem. {\it $rg(E,A)=n+d(A)$, $E$ – denotes the identical matrice.