Why do we use matrices to solve equations? Why not just manipulate then symbolically as trees?
>>16814530>Why not just manipulate then symbolically as trees?elaborate
>>16814565Rather 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.
>>16815446I like to use beads and chits to represent value in my commercial transactions.Do you expect surplus harvests this year?
>>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.
>>16815531Hmm the second point makes sense, but doesn't the first just boil down to simple tree operations for symbolic computation? Like the kind you'd do in a lisp?
kek it takes the same amount of work to do a matrix vs substitution. especially if you have to deal uncommon fractions
>>16815694Imagine the disgusting person she had to befriend to even know about this disgusting shit.
>>16815664> but doesn't the first just boil down to simple tree operations for symbolic computation?Yes, but it will inevitably be slower than Gaussian elimination. Let's say you have an n-dimensional matrix equation, Ax=b, and you need to solve it for x. If this thread still exists in the morning I'll write up some latex to explain why.
>>16815694>quirky chungus scene kid gfYike
>>16814530Because it's normally less efficient and more convoluted. Maybe do trees if you know you will have very sparse matrices. Then you can take a hit in tree overhead to save a lot of redundant reading and writing of null values.
>>16814530Mathematicians are lazy people. They will always find a way to optimize things. Matrices are good when you have a system with Many I mean MANY equations (10 ,50, 100)
