Question: Let A and B be 3x3 matrices such that \(\det \left( 4{{B}^{2}}+5B \right)=7\) and A is row equivalent to

\[\left[ \begin{matrix} 1 & 4 & 1 \\ 2 & 5 & -2 \\ 3 & 6 & 1 \\ \end{matrix} \right]\]

Let \({{A}^{t}}B{{A}^{2}}{{B}^{t}}=[{{v}_{1}},{{v}_{2}},{{v}_{3}}]\), is there a vector b, that lives in \({{\mathbb{R}}^{3}}\) such that b is not in the span of (v₁, v₂, v₃)