Hw 6.2   Q29

There are total of 15 steps.  I will only post those procedures since it will be too long to post the entire solution.

Pivot element: 1 fourth row and second colm.  Basic Var: S1,S2,S3,S4,P.

Step I:

5R₄ +R₅ ->  R₅

 Step II:

-4R₄ +R₃ -> R₃

Step III:

-3R₄ +R₂ ->R₂ 

Step IV:

-2R₄ +R₁ ->R₁   

Second Pivot:

Pivot Element: 1 first col and third row.  Basic element: S1,S2,S3, X2,P.

Step V:

-R₃ +R₁->R₁

Step VI:

-R₃ +R₂ ->R₂

Step VII:

2R₃ +R₅ ->R₅

Third Pivot:

Pivot element: 1 sixth colm and second row.  Basic var: S1,S2,X1,X2,P.

Step VIII:

-2R₂ +R₁ -> R₁

Step IX:

4R₂ +R₃ ->R₃

Step X:

-R₂ +R₄ ->R₄

Step XI:

3R₂ + R₅ -> R₅

 Fourth Pivot:

Pivot element: 1, fifth col and first row.

Basic Var: S3,S4,X1,X2, P.

Step XII:

R₁ + R₂ ->R₂

 Step XIII:

3R₁ +R₃ -> R₃

Step XIV:

-R₁ + R₄ ->R₄

Step XV:

R1+ R5 -> R5.

Then set: S1=0 and S2=0.

Solve the following with the above conditions:

S₁ - 2S₂ + S₃  =4

S₁ + S₄ =6

X₁ +3S₁ =24

X₂ - S₁ =8

S₁  + S₂ + P = 88