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Algrebra Math

Problem from mathematical quickies – #264 – More simultaneous equations

Ok, so I just ground through this solution long hand – which sucks because I am fairly sure there was some slick trick I was supposed to have seen here. All the problems in this book are searching for an elegant solution and this one is anything but. I should ask Konrad what I missed when he gets back.

Solve the four equations with four unknowns
Solve the four equations with four unknowns

…. and it keeps going, and going, and going…. I am really missing something here. This will give me the right solution but *ick*. 

Solution continued
Solution continued

One reply on “Problem from mathematical quickies – #264 – More simultaneous equations”

Konrad got back to me with an insightful comment….

There is a lot of symmetry in the problem, so it is pretty obvious that x1 = -x4 and x2 = -x3. Making those substitutions turns the problem into the much simpler

[-4 4][x1] = [ 16]
[ 6 -2][x2] [-16]

Since we know how to invert a 2×2 matrix, the answer is just
[x1] = (1/16)[2 4][ 16] =[-2]
[x2] [6 4][-16] [ 2]

so x1 = x3 = -2, x2 = x4 = 2

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