Here's what I would have submitted:

Question 1:

[1   3  3 -2 13]
[-2  1 -1  2 -2]
[-1 -4  0 -2 17]
[-1 -1 -4  5 34]



Question 2:
subtract row 1 from row 2:
[ 1 4 -3 -3 -27]
[ 0 1  2 -1   5]
[-3 1  5 -4  26]
add 3 * row 1 to row 3:
[1  4 -3  -3 -27]
[0  1  2  -1   5]
[0 13 -4 -13 -55]
subtract 13*row 2 from row 3:
[1 4  -3 -3  -27]
[0 1   2 -1    5]
[0 0 -30  0 -120]
now it's in echelon form!



Question 3:

It has infinitely many solutions:  Solutions exist because there's no
pivot in the last column.  Also there's no pivot in the fourth column,
so it has a free variable.