Hello, I was wondering if there was a way that I could figure out what numbers w

Question

Hello,

     I was wondering if there was a way that I could figure out what numbers would work out best when manipulating a matrix to find the answer to linear systems. I usually end up getting the answer in due time, but I don't feel completely confident that I will be able to find the answer when taking an exam. I would appreciate it if anyone could help me figure out a way in which I would be able to quickly reduce the matrix. If there is no definite way, then can anyone give me any advice as to how they go about trying to solve these matrices (i.e. which row to do first, etc). Examples would be appreciated. ^_^ Thanks in advance!

Explanation / Answer

It's not what you are going to want to hear (or in this case read), but there isn't really a "shortcut" way to do this. Row manipulation (Gauss-Jordan elimination) is the fastest way, and the only way to make that faster is to practice until you start seeing the shortest distance from start to finish. I always like to make the first column [1;0;0;0;...;0], and then work my way over to the second column to make it [0;1;0;0;0;...;0], and the third column [0;0;1;0;0;0;...0], etc. That is about the 'cheapest' way I have discovered to doing these. I hope this helps! If you are able to do the problem, don't change anything just practice until it gets faster! Also, there is no real "example" way of doing these because each problem is just different enough that whatever the example given takes to solve won't be used to solve the next one.

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