The first step I would do is:
This is quite a complicated one! I'll leave the last steps for you to do. (Hint, it starts with .
We want to reduce the first three columns to the identity matrix and I recommend working one column at a time.
We want "1 0 0" in the first column. Since there is a "4" in first column, first row, multiply the first row by 1/4. Since there is a "5" in first column, second row, subtract 5 times the new first row from the second row. Since there is a "-4" in the first column, third row, add 4 times the new first row to the third row:
In order to get a "1" in second column, second row, we must multiply the second column by -2/3. Then add 1/2 the new second row to the first row and add 3 times the new second row to the third row:
Finally, multiply the third row by 3/4 to get a "1" in the third column, third row, subtract 4/3 the new third row from the first row and subtract 13/6 the new third row from the second row: