Find the basis for the image of the matrix B

B = 4 2 2 0

0 3 -1 1

1 -3 4 2

So first i transposed it B'

4 0 1

2 3 -3

2 -1 4

0 1 2

then i reduced it to echelon form

divide top row by 4

1 0 1/4

2 3 -3

2 -1 4

0 1 2

row 2 - 2 x row1

row 3 - 2 x row 1

1 0 1/4

0 3 -7/2

0 -1 7/2

0 1 2

make rows 2 and 3 start with 1

1 0 1/4

0 1 -7/6

0 1 -7/2

0 1 2

row 3 - row 2

row 4 - row 2

1 0 1/4

0 1 -7/6

0 0 -14/6

0 0 19/6

make row 3 and 4 start with 1

1 0 1/4

0 1 -7/6

0 0 1

0 0 1

row 4 - 3

1 0 1/4

0 1 -7/6

0 0 1

So these are the basis, is this right? Have i done the ecehlon form right?