Last week in my chemistry class, I was exposed to Hess’ Law and while doing some example problems in class, I immediately wondered if there was some way to apply linear algebra to automagically solve the equations. I asked my professor if he knew if linear algebra could be applied to solve them, but he said he was unsure since he’s actually not a math person.

I really hate throwing things like that out in class where it doesn’t really apply to what’s being taught (you know, those jerks that ask these stupid wiseguy questions in class just to look like they know more than everyone else), but I just had to get some affirmation if it was possible.

During the weekend I tried to see if I can do it with matrix operations, but I eventually realized that the linear algebra I know is too limited to find a solution. I’ve completely mapped out what the problem looks like, I know how it can be solved via human guess and check, but I really feel there’s a set of consistent mathematical operations that would just give me what I need (kind of like gaussian elimination to solve linear systems of equations).

If anyone knows the algorithm, I will give $100 USD to the first person who does. Note that I’ve also posted this on LinkedIn, meaning whoever is the first, gets it. The algorithm needs to be able to solve all matrices that can be assembled from problems found in Hess’ Law without human intervention (other than inputting initial and final values of the problem). What I’m looking for is an automatic generation of the intermediate Xn values that are required to multiply each row to get the final values.

**Edit 1: **Piyush Pant discovered that Wolfram Alpha can be used to solve these problems. However, it does not give the algorithm.

http://www95.wolframalpha.com/input/?i=Solve+{w,x,y,z}.{{1,0,0,-3,-1,3,0},+{0,2,3,0,-1,0,0},+{0,0,1,0.5,0,0,-1},{0,0,0,0,0,-1,1}}%3D{-2,4,0,3,0,0,0}

Here is an actual application of this possible algorithm:

Solution: http://www95.wolframalpha.com/input/?i=Solve+{w%2Cx}.{{1%2C3%2C-2%2C-3%2C0}%2C+{0%2C3%2C-2%2C-2%2C1}}%3D{-1%2C0%2C0%2C1%2C1}

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