>>16815446
> Rather than represent a system of equations as a grid of coefficients, we just write the equations and then solve them normally, performing substitutions, crossing things out, etc.
Well, the main reason is that it's super easy to solve matrix algebra problems on a computer. When you do a Gaussian elimination, you get all of your variable values at once.
Secondly, if you do it in a sequence/tree, you now introduce a dependency/order arbitrarily in your solution process. This makes it so that you've now made getting the exact same solution on the computer (given limited floating point precision) dependent on the specific order of solution.
