Row Reduction & Rank · Hard problem

A beam's stiffness matrix is $A=\begin{pmatrix}4&2&0\\2&3&1\\0&1&2\end{pmatrix}$, relating three node loads $\mathbf b$ to deflections $\mathbf x$ via $A\mathbf x=\mathbf b$. A first load $\mathbf b_1=(8,11,8)$ produces deflections $\mathbf x_1$; a separate, second load $\mathbf b_2=(10,8,3)$ produces deflections $\mathbf x_2$. By superposition, find the combined deflection at node $3$ (that is, $x_{1,3}+x_{2,3}$) when both loads act together.