SOLUTION: solve the following linear equations using matrix techniques: 3x1+5x2=1 x1+2x2=2

   3   5   1
   1   2   2
Since a 1 in row 1 column 1 is desired, I'll swap the rows:
   1   2   2
   3   5   1
Adding -3 times row 1 to row 2:
   1   2   2
   0  -1  -5
Adding 2 times row 2 to row 1:
   1   0  -8
   0  -1  -5
Multiplying row 2 by -1:
   1   0  -8
   0   1   5