Use language and implement matrix operations with matrices as a tool for the treatment of situations to handle structured data in tables or graphs.
know the basic vocabulary for the study of matrices, element, row, column, diagonal, etc.
matrix is \u200b\u200bcalled to any set of numbers or terms arranged in a rectangular, forming rows and columns.
Each of the numbers making up the matrix element is called . One element is distinguished from another by its position, ie row and column to which it belongs.
The number of rows and columns of a matrix is \u200b\u200bcalled dimension of a matrix.
The set of matrices of m rows and n columns is denoted by A mxn or (a Ij ) , and any element thereof, which is in row i in column j, ij to .
Two matrices are equal when they have the same dimension and the elements that occupy the same place in both, are equal.
Calculate sums of matrices, scalar product of matrices and matrix products. The emphasis on non-commutativity of matrix multiplication.
Solve matrix equations.
Solve systems of linear inequalities with two unknowns, with at most three inequalities, in addition to the restrictions of no negativity of the variables, if any.
know the basic terminology linear programming, objective function, feasible region and optimal solution.
Linear programming responds to situations requiring maximize or minimize functions that are subject to certain limitations, we call restrictions.
Its use is common in industrial applications, economics, military strategy, etc..
objective function
Essentially linear programming is optimize (maximize or minimize) an objective function , a linear function of several variables:
f (x, y) = ax + by . Restrictions
The objective function is subject to a number of restrictions expressed by linear inequalities :
 | to 1 1 x + b y ≤ c 1 |
| to 2 x + b 2 and 2 ≤ c | |
| ... ... ... | |
| to n x + b y ≤ c n n |
Each inequality constraint system determines a half-plane.
The feasible solution set intersection of all half-planes formed by the restrictions, determines a site, bounded or not, called validity region or area feasible solutions. Optimal solution
The set of vertices of the enclosure set called basic feasible solutions and the apex which shows the optimal solution called ultimate solution (or minimum as appropriate). ;
determine the vertices of the feasible region linear programming problem and draw it.
Solve linear programming problems in two variables, from various backgrounds, social,
economic or demographic, analytical and graphical means with bounded feasible regions. Interpret solutions.
If the variables involved are whole may be regarded as continuous throughout the process of resolution.
Steps to solve a linear programming problem:
1. Choose unknowns.
2. Write objective function depending on the problem data.
3. Write restrictions as a system of inequalities.
4. Find all feasible solutions by plotting restrictions.
5. Calculate the coordinates of the vertices of the compound of feasible solutions (if they are few).
6. Calculate the value objective function in each of the vertices to see which of them represent the maximum or minimum value as we ask the problem (keep in mind here the possible non-existence of solution if the enclosure is unbounded).
