Linear Algebra and the C Language/a08a

${\displaystyle \mathrm {x_{1}C_{3}H_{8}+x_{2}O_{2}\longrightarrow x_{3}CO_{2}+x_{4}H_{2}O} }$

a) The system:

double ab[RA*(CA+C1)]={
//  x1   x2   x3   x4      b
    
    +0,  +0,  -0,  -0,     0, //C
    +0,  +0,  -0,  -0,     0, //H
    +0,  +0,  -0,  -0,     0, //O      
};

• Each coefficient must have a column. Here four coefficients therefore four columns.
• Each atom must have a row. Here, three atoms, so three rows.
• The coefficients on the left side of the chemical equation must have a positive coefficient. (x1, x2)
• The coefficients on the right side of the chemical equation must have a negative coefficient. (x3, x4)

b) The first column:

${\displaystyle \mathrm {x_{1}C_{3}H_{8}} }$

double ab[RA*(CA+C1)]={
//  x1   x2   x3   x4      b

    +3,  +0,  -0,  -0,     0, //C
    +8,  +0,  -0,  -0,     0, //H
    +0,  +0,  -0,  -0,     0, //O      
};

• x1 is related to two atoms C and H.
• There is three C that we write in the first column of the first row.
• There are eight H that we write in the first column of the second row.

c) The second column:

${\displaystyle \mathrm {x_{2}O_{2}} }$

double ab[RA*(CA+C1)]={
//  x1   x2   x3   x4      b

    +3,  +0,  -0,  -0,     0, //C
    +8,  +0,  -0,  -0,     0, //H
    +0,  +2,  -0,  -0,     0, //O      
};

• x2 is related to one atome O.
• There are two O that we write in the second column of the third row.

d) The third and the fourth columns: (With negative coefficients)

${\displaystyle \mathrm {x_{1}C_{3}H_{8}+x_{2}O_{2}\longrightarrow x_{3}CO_{2}+x_{4}H_{2}O} }$

double ab[RA*(CA+C1)]={
//  x1   x2   x3   x4      b

    +3,  +0,  -1,  -0,     0, //C
    +8,  +0,  -0,  -2,     0, //H
    +0,  +2,  -2,  -1,     0, //O             
};

Now we need to introduce this system into the file: c00a.c.