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

# Example 2 - Linear Eqs.
# Biological Reactors
# Verified Solution: a = 0.231648, b = 0.163132,
# c = 0.652529 # d=0.59217, e = 0.347471
# Ref.:Prob. 2.3 in Problem Solving in Chemical...

c+e=1
3*b-2*c-2*d=-2
2*a-0.27*c-d-2*e=-1
b=0.25*c
1.5*a = e


Linear equations solution

    Variable Value
1 c 0.65252855
2 e 0.34747145
3 b 0.16313214
4 d 0.59216966
5 a 0.23164763

Linear equations

  + c e = 1
  3 b 2 c 2 d = 2
  2 a 0 . 2 7 c d 2 e = 1
  b = 0 . 2 5 c
  1 . 5 a = e

Coefficients matrix and beta vector

    c e b d a beta
1 1 1 0 0 0 1
2 -2 0 3 -2 0 -2
3 -0.27 -2 0 -1 2 -1
4 -0.25 0 1 0 0 0
5 0 -1 0 0 1.5 0

General

Number of equations: 5
Reporting digits: 10