Here's what I would have submitted:


Question 1:

det G =
  | 1  2   1   3|     |1  2   1   3|      |1  2   1   3|
3*| 3 10  19  29| = 3*|0  4  16  20|= 12* |0  1   4   5|
  | 0 -2  -7  -8|     |0 -2  -7  -8|      |0 -2  -7  -8|
  |-2 -7 -18 -31|     |0 -3 -16 -25|      |0 -3 -16 -25|

      |1 2  1   3|      |1 2 1  3|
= 12* |0 1  4   5| = 12*|0 1 4  5| = -24
      |0 0  1   2|      |0 0 1  2|
      |0 0 -4 -10|      |0 0 0 -2|



Question 2:

By Cramer's rule, the entries of x will be the determinant of some
integer matrix divided by the determinant of G, so they'll be integers
divided by -24.  Thus they won't necessarily all be integers, but
their denominators will all be divisible by 24.



Question 3:

To use Cramer's rule, I would have to find the determinants of five
matrices, each of which would require me to do a row-reduction.  

To use row-reduction, I would simply have to row-reduce G.

To use Cramer's rule, I would have to row-reduce G and then row-reduce
four other matrices.

Row-reduction is faster.