So it's just a few days before my math exam and I came across this excercise and I just can't seem to find the right answer. Would really appreciate your help on this one.
It's from a german textbook so please excuse any grammar mistakes:
d 'is celebrating a party. a, b and c are doing a drinking game. They all drink the same from same size glasses:'
I: a and b together drank as much as c. II: a and c together drank 4 times as much as b III: a drank n more glasses then b
1) I need to find out the Linear System of Equations.
So I would assume:
I: a + b = c II: a + c = 4b III: b + n = a
To write the matrix it in the form of: A*X = B:
=> I: a + b - c = 0 => II: a - 4b + c = 0 => III: -a + b + n = 0
(please correct if I'm wrong)
next: 2) Find the inverse Matrix with the Gauß-Jordan-Algorithm
Is that correct? This is where I had a lot of problems with. Because of that extra variable n in the matrix.
3) From that inverse matrix i have to find universal solution where I just have to put in n to solve.
Don't really know what to do here. If I take my inverse matrix and multiply it by B wich is (0 0 0) all my values for a,b,c would get 0...
So don't really know how to proceed...
4) I just need to try different values for n and show the Equations for different n values.
Would really really appreciate any kind of help. I've been working on this for more than 3 hours and I just can't seem to find the answer.
Thank you in advance !