I have the following matrix equality: $\left( \begin{array}{ccc} u_{11} & u_{12} & -p_1 \\ u_{21} & u_{22} & -p_2 \\ p_1 & p_2 & 0 \end{array} \right).\left( \begin{array}{c} \text{dc}_1 \\ \text{dc}_2 \\ \text{d$\lambda $} \end{array} \right)=\left( \begin{array}{c} 0 \\ 0 \\ \text{dI} \end{array} \right)$
I need to solve for $\frac{\text{dc}_1 }{\text{dI}},\frac{ \text{dc}_2}{\text{dI}},\frac{\text{d$\lambda $}}{\text{dI}}$.
Attempt: I tried using Cramer's rule, but all I get is the solution for $dc_1,dc_2,d\lambda$. I need to find the solution for the $dc_1,dc_2,d\lambda$ over $dI$. Any hints please.