= Solution
Choose a fixed reference <basis> and let $V,W$ have columns $v_i,w_i$. Both <matrices> are invertible. The vectors $v_i+\lambda w_i$ are dependent exactly when $\det(V+\lambda W)=0$. This is a <polynomial> in $\lambda$ of degree $m$, whose leading <coefficient> is $\det W\ne0$. A nonzero degree-$m$ <polynomial> has at most $m$ distinct real roots. Thus \b[there are at most $m$ exceptional parameters]. This is the <determinant> argument for the <matrix pencil> $V+\lambda W$.
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