Linear Algebra and the C Language/a08a

Balancing a chemical equation

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

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:

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

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:

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

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)

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

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.