So I got this problem in which I had to determine whether a vector [1,2,5,-1] was in the row space of the following matrix:

First row: 2, -1, 0, 3

2nd row: 7, -1, 5, 8

I know that in order to do this problem, you have to set up the matrix:

2 7 |1

-1 -1 | 2

0 5 | 5

3 8 | - 1

I row reduced it using row-reduced echelon form, and I was wondering if I got a correct answer (my graphic calculator doesn"t work for some reason when I create matrices in which the number of rows exceed the number of columns so I couldn't use it to check my work).

Using Type I (what you use to turn a pivot entry to 1) and Type II (what you use to turn a number into 0, which means taking the negative of the desired entry, multiplying it by the pivot row, and adding the row with the desired entry) row operations, I finally wound up with the matrix:

1 0 | 5/3

0 1 | -1/3

0 0 | 20/3

0 0 | -10/3