# Solving a system of equations with additional condition

Suppose I have the following system I want to solve

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

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.

• 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. Mar 30, 2022 at 23:12
• I will try this. Thank you
– WHN
Mar 30, 2022 at 23:13
• The determinant of your matrix is $0$. Do you know what that means? Mar 30, 2022 at 23:26
• That the columns of my matrix are linearly dependent?
– WHN
Mar 31, 2022 at 1:21