L inear Programming

1. 利用 Onlinetool 作矩陣運算並處理線性規劃問題 Linear Programming

2. Matrix computation • http://www.bluebit.gr/matrix-calculator/ • This is a online tool for matrix calculator

3. Matrix computation • Matrix 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

4. Matrix computation • General system of linear equation : ax + by + cz = k1 dx + ey + fz = k2 gx + hy+iz = k3 • Solving linear equation by AX =b • Where

5. Matrix computation • 當 A 的反矩陣存在，則有唯一解 x , y, z 為 • X = A-1 *b • Thus,

6. Matrix computation • For example : • x + 2y + 3z = 2 • x + + z = 3 • x + y - z = 1

7. Matrix computation • Solution: • Show in online matrix calculator

8. Matrix computation • Using 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);

9. Linear programing • Help : 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] );

10. Linear programing • Help : Topic search > linearprogramming • with(Optimization): • LPSolve(-4*x-5*y, {2*x + y <= 2, x - y <= 2,x=-2});