Linear Programming

利用 Online tool 作矩陣運算並處理線性規劃問題

Matrix computation

http://www.bluebit.gr/matrix-calculator/

This is a online tool for matrix calculator

Matrix computationMatrix Transpose : 轉置矩陣

Matrix Inverse : 反矩陣

Determinant calculation : 行列式值

Matrix Multiplication : 矩陣乘法

Systems of linear equation : 線性方程組

Matrix computationGeneral system of linear equation :

ax + by + cz = k1dx + ey + fz = k2gx + hy + iz = k3

Solving linear equation by AX =b Where

3

2

1

,

k

k

k

b

ihg

fed

cba

A

Matrix computation當 A 的反矩陣存在，則有唯一解 x , y, z 為

X = A-1 *b

Thus,

3

2

1

a

1-

k

k

k

ihg

fed

cb

z

y

x

Matrix computationFor example :

x + 2y + 3z = 2x + + z = 3x + y - z = 1

1

3

2

,

111

101

321

bA

Matrix computationSolution:

Show in online matrix calculator

2

11

2

5

X

Matrix computationUsing Maple to solve matrix computation

> with(LinearAlgebra):> m:=Matrix([[1, 2, 3],[1, 0, 1],[1, 1, -1]]);> b:=Vector([2, 3, 1]);> LinearSolve(m, b);

Linear programingHelp : Topic search > Linearsystemplot

with(Student[LinearAlgebra]): infolevel[Student[LinearAlgebra]] := 1:sys := {2*x + y = 2, x - y = 2,x=-2};LinearSystemPlot( sys );LinearSystemPlot( sys, [x,y,z] );

Linear programingHelp : Topic search > linearprogramming with(Optimization):LPSolve(-4*x-5*y, {2*x + y <= 2, x - y <=

2,x=-2});