basis
Basis is a square matrix composed of linearly independent column vectors in coefficient matrix A. These column vectors are called basis vectors, and there can be several according to different choices. When calculating the number of bases, we will group the bases with the same column vector. But in actual calculation, we need to pay special attention to the order of column vectors in the base.
basic variable
When we determine the basis, the corresponding basic variables and non-basic variables are also determined. The vector composed of base variables is in the same order as the column vectors in the base.
Basic solution
When we determine the basis, we set the non-base variable to 0, and then calculate the value of the base variable. This is the basic solution. We can also use the formula B XB = b to solve it, because the foundation is reversible, so XB = XB = b-1b.
Linear programming problem
The linear programming problem is to find the maximum value of the objective function under constraints. The optimal solution is the solution that maximizes or minimizes the objective function. The steps to solve the optimal solution include setting variables, establishing objective function, listing constraints, drawing feasible regions and determining the optimal solution.