PolymathPlus Report
📑   Linear Equations 2022-04-01 18:49 

# Example 3 - Linear Eqs. Steady State Material Balances
# Verified Solution: D1=26.25, B1=17.5, D2=8.75, B2=17.5
# Ref.: Comput. Appl. Eng. Educ. 6: 172-173, 1998

.07*D1 + .18*B1 + .15*D2 + .24*B2 = 0.15*70
.04*D1 + .24*B1 + .1*D2 + .65*B2 = 0.25*70
.54*D1 + .42*B1 + .54*D2 + .1*B2 = 0.40*70
.35*D1 + .16*B1 + .21*D2 + .01*B2 = 0.20*70


Linear equations solution

    Variable Value
1 D1 26.25
2 B1 17.5
3 D2 8.75
4 B2 17.5

Linear equations

  + + + . 0 7 D 1 . 1 8 B 1 . 1 5 D 2 . 2 4 B 2 = 0 . 1 5 7 0
  + + + . 0 4 D 1 . 2 4 B 1 . 1 D 2 . 6 5 B 2 = 0 . 2 5 7 0
  + + + . 5 4 D 1 . 4 2 B 1 . 5 4 D 2 . 1 B 2 = 0 . 4 0 7 0
  + + + . 3 5 D 1 . 1 6 B 1 . 2 1 D 2 . 0 1 B 2 = 0 . 2 0 7 0

Coefficients matrix and beta vector

    D1 B1 D2 B2 beta
1 0.07 0.18 0.15 0.24 10.5
2 0.04 0.24 0.1 0.65 17.5
3 0.54 0.42 0.54 0.1 28
4 0.35 0.16 0.21 0.01 14

General

Number of equations: 4
Reporting digits: 10