Convert the following matrix to reduced row echelon form 0 1

Convert the following matrix to reduced row echelon form [0 -1 3 1 3 2 1 0 -2 6 1 -5 0 -1 0 3 -9 2 4 1 -1 0 1 -3 -1 3 0 1]

Solution

Row Operation 1:   0 -1 3 1 3 2 1 0 -2 6 1 -5 0 -1 0 3 -9 2 4 1 -1 0 1 -3 -1 3 0 1 multiply the 1st row by -1 0 1 -3 -1 -3 -2 -1 0 -2 6 1 -5 0 -1 0 3 -9 2 4 1 -1 0 1 -3 -1 3 0 1 Row Operation 2:   0 1 -3 -1 -3 -2 -1 0 -2 6 1 -5 0 -1 0 3 -9 2 4 1 -1 0 1 -3 -1 3 0 1 add 2 times the 1st row to the 2nd row 0 1 -3 -1 -3 -2 -1 0 0 0 -1 -11 -4 -3 0 3 -9 2 4 1 -1 0 1 -3 -1 3 0 1 Row Operation 3:   0 1 -3 -1 -3 -2 -1 0 0 0 -1 -11 -4 -3 0 3 -9 2 4 1 -1 0 1 -3 -1 3 0 1 add -3 times the 1st row to the 3rd row 0 1 -3 -1 -3 -2 -1 0 0 0 -1 -11 -4 -3 0 0 0 5 13 7 2 0 1 -3 -1 3 0 1 Row Operation 4:   0 1 -3 -1 -3 -2 -1 0 0 0 -1 -11 -4 -3 0 0 0 5 13 7 2 0 1 -3 -1 3 0 1 add -1 times the 1st row to the 4th row 0 1 -3 -1 -3 -2 -1 0 0 0 -1 -11 -4 -3 0 0 0 5 13 7 2 0 0 0 0 6 2 2 Row Operation 5:   0 1 -3 -1 -3 -2 -1 0 0 0 -1 -11 -4 -3 0 0 0 5 13 7 2 0 0 0 0 6 2 2 multiply the 2nd row by -1 0 1 -3 -1 -3 -2 -1 0 0 0 1 11 4 3 0 0 0 5 13 7 2 0 0 0 0 6 2 2 Row Operation 6:   0 1 -3 -1 -3 -2 -1 0 0 0 1 11 4 3 0 0 0 5 13 7 2 0 0 0 0 6 2 2 add -5 times the 2nd row to the 3rd row 0 1 -3 -1 -3 -2 -1 0 0 0 1 11 4 3 0 0 0 0 -42 -13 -13 0 0 0 0 6 2 2 Row Operation 7:   0 1 -3 -1 -3 -2 -1 0 0 0 1 11 4 3 0 0 0 0 -42 -13 -13 0 0 0 0 6 2 2 multiply the 3rd row by -1/42 0 1 -3 -1 -3 -2 -1 0 0 0 1 11 4 3 0 0 0 0 1 13  42 13  42 0 0 0 0 6 2 2 Row Operation 8:   0 1 -3 -1 -3 -2 -1 0 0 0 1 11 4 3 0 0 0 0 1 13  42 13  42 0 0 0 0 6 2 2 add -6 times the 3rd row to the 4th row 0 1 -3 -1 -3 -2 -1 0 0 0 1 11 4 3 0 0 0 0 1 13/42 13/42 0 0 0 0 0 1/7 1/7 Row Operation 9:   0 1 -3 -1 -3 -2 -1 0 0 0 1 11 4 3 0 0 0 0 1 13  42 13  42 0 0 0 0 0 1  7 1  7 multiply the 4th row by 7 0 1 -3 -1 -3 -2 -1 0 0 0 1 11 4 3 0 0 0 0 1 13/42 13/42 0 0 0 0 0 1 1 Row Operation 10:   0 1 -3 -1 -3 -2 -1 0 0 0 1 11 4 3 0 0 0 0 1 13  42 13  42 0 0 0 0 0 1 1 add -13/42 times the 4th row to the 3rd row 0 1 -3 -1 -3 -2 -1 0 0 0 1 11 4 3 0 0 0 0 1 0 0 0 0 0 0 0 1 1 Row Operation 11:   0 1 -3 -1 -3 -2 -1 0 0 0 1 11 4 3 0 0 0 0 1 0 0 0 0 0 0 0 1 1 add -4 times the 4th row to the 2nd row 0 1 -3 -1 -3 -2 -1 0 0 0 1 11 0 -1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 Row Operation 12:   0 1 -3 -1 -3 -2 -1 0 0 0 1 11 0 -1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 add 2 times the 4th row to the 1st row 0 1 -3 -1 -3 0 1 0 0 0 1 11 0 -1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 Row Operation 13:   0 1 -3 -1 -3 0 1 0 0 0 1 11 0 -1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 add -11 times the 3rd row to the 2nd row 0 1 -3 -1 -3 0 1 0 0 0 1 0 0 -1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 Row Operation 14:   0 1 -3 -1 -3 0 1 0 0 0 1 0 0 -1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 add 3 times the 3rd row to the 1st row 0 1 -3 -1 0 0 1 0 0 0 1 0 0 -1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 Row Operation 15:   0 1 -3 -1 0 0 1 0 0 0 1 0 0 -1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 add 1 times the 2nd row to the 1st row 0 1 -3 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 1 0 0 0 0 0 0 0 1 1