Suppose I have the following system I want to solve

\begin{equation} \begin{bmatrix} -\frac{1}{4} & \frac{5}{12} & 1\\ -\frac{1}{3} & \frac{1}{2} & 1\\ -\frac{5}{12} & \frac{7}{12} & 1 \end{bmatrix}\cdot \begin{bmatrix} \delta_0\\ \delta_1\\ \delta_2 \end{bmatrix}=\begin{bmatrix} 1.5000 \\ 1.6667\\ 1.8333 \end{bmatrix} \end{equation}

Where additionally $\delta_0<2\delta_1$

If I used a program such as R and Matlab to try to solve this. Unfortunately, to find a solution of the system. This is because I am unable/ do not know how to incorporate the additional condition $\delta_0<2\delta_1$ when solving the system.

I would like to find the values of $\delta_0, \delta_1, \delta_2$. Unfortunately I get stuck.

  • $\begingroup$ Could you just solve the linear system first, then amongst the solutions to that system figure out which ones also satisfy your inequality? Particularly if you make $\delta_0$ or $\delta_1$ the free variable of your solution it seems you could do this. $\endgroup$ Mar 30, 2022 at 23:12
  • $\begingroup$ I will try this. Thank you $\endgroup$
    – WHN
    Mar 30, 2022 at 23:13
  • $\begingroup$ The determinant of your matrix is $0$. Do you know what that means? $\endgroup$ Mar 30, 2022 at 23:26
  • $\begingroup$ That the columns of my matrix are linearly dependent? $\endgroup$
    – WHN
    Mar 31, 2022 at 1:21


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