Variable: | P | P^{*}_{1} | p_{1} | P^{*}_{2} | x_{2} | p_{2} |
Equation (1) | x | |||||
Equation (2) | x | x | ||||
Equation (3) | x | |||||
Equation (4) | x | x | x | |||
Equation (5) | x | |||||
Equation (6) | x | x | x |
It was noted that the equations could be solved in the order:
Variable: | P | P^{*}_{1} | p_{1} | P^{*}_{2} | x_{2} | p_{2} |
Equation (1) | x | |||||
Equation (3) | x | |||||
Equation (5) | x | |||||
Equation (2) | x | x | ||||
Equation (4) | x | x | x | |||
Equation (6) | x | x | x |
It should now be clear that no equation contains more than one variable other than those already solved for in the equation rows above it.
This is particularly obvious if we now also reorder the columns, each of which corresponds to a variable, into the sequence for which the variables will be solved, viz:
Variable: | P^{*}_{1} | P^{*}_{2} | x_{2} | p_{1} | p_{2} | P |
Equation (1) | x | |||||
Equation (3) | x | |||||
Equation (5) | x | |||||
Equation (2) | x | x | ||||
Equation (4) | x | x | x | |||
Equation (6) | x | x | x |
This is described as being lower triangular as all the non-zero entries fall in the bottom left of the table.
The entries along the diagonal indicate the variables for which each equation is solved by rearrangement into a formula.
All variables below the diagonal have been solved for in earlier equations.