How to solve AX<=B, Where A is rectangualr matrix and b is vertical matrix

How to Matlab program for solving AX<=B, Where A is rectangular matrix and b is vertical matrix. For example: Find the set x of given AX<=B, where A=[1 2;6 5],B=[2 1]',X=[x1 x2]'. Please help me.

Answer 1

[Santa Raghavan]

If you only have a system of inequalities your solution is generally not a point but an area (or volume...).

1. If you want a maximum feasible or minimum infeasible bounds for your system:

The linear programming (or linprog) in the optimization toolbox can compute feasible points of linear inequality systems (use f=0 as objective function). Finding the maximal feasible or minimal infeasible system is a mixed zero-one linear problem. If the number of inequalities is not too large you can use fminconset which is an extension of fmincon for this task.

Refer: https://www.mathworks.com/help/optim/ug/linprog.html

2. If you want a visual solution

The Symbolic Math toolbox lets you plot inequalities and color codes region of interest.

plot::Inequality([ineq1, …], x = xmin .. xmax, y = ymin .. ymax, <a = amin .. amax>, options)

Here is a useful link for the same: https://www.mathworks.com/help/symbolic/mupad_ref/plot-inequality.html