Question 174542
I have a feeling no one is helping you on this because we are all stumped by it too!!  I'm retired, and particularly bored today, so I thought I would give it a looksee!  I would say first of all, for you to go with your calculator solution!!


I haven't worked with matrices for a VERY long time, but, if your equations are correct and I think they are correct, you need to convert from this system of equations to one in which you have eliminated coefficients to leave 0s and 1s.  You may have to try a few times and I must admit that I didn't get the calculator answers the first time.  This is what I did.  First, reduce the equations to smaller numbers:

10a +  4b + 12c = 120  (Divide by 2)
11a + 77b +  0c = 220  (Divide by 11)
 4a +  1b + 16c =  80


 5a +  2b + 6c =  60
  a +  7b + 0c =  20  (Mult by -4 and add to eq #3)
 4a +  1b + 16c = 80


5a +  2b + 6c =  60
  a +  7b + 0c =  20  (Mult by -5 and add to eq #1)
 0a - 27b + 16c = 0


5a +  2b + 6c =  60
 0a - 33b + 6c = -40  
 0a - 27b + 16c = 0


Next, eliminate the b coefficients by multiplying Eq #2 times -27 and Eq #3 times  33 and add together.  (The first two equations remain the same!)

5a +  2b + 6c =  60
 0a - 33b + 6c = -40  
 0a + 0b + 366c = 1080



Next, divide the Eq #3 by 366:

5a +  2b + 6c =  60
 0a - 33b + 6c = -40  
 0a + 0b + 1c = 1080/366


So, c= 1080/366 = 2.9508 approximately, which is the calculator value that I got.  I'm sure you can finish this now.  By the way, my other calculator values were a=7.759 and b= 1.7486 approximately.


Good luck!!


R^2