Find Reduced Row Echelon Form [[2,2,2,0],[-2,5,2,1],[8,1,4,-1]]

Problem

[[2,2,2,0],[−2,5,2,1],[8,1,4,−1]]

Solution

1. Divide the first row by 2 to create a leading 1 in the first column.

(R_1)→1/2*(R_1)

[[1,1,1,0],[−2,5,2,1],[8,1,4,−1]]

2. Eliminate the entries below the leading 1 in the first column by adding 2 times the first row to the second row and subtracting 8 times the first row from the third row.

(R_2)→(R_2)+2*(R_1)

(R_3)→(R_3)−8*(R_1)

[[1,1,1,0],[0,7,4,1],[0,−7,−4,−1]]

3. Divide the second row by 7 to create a leading 1 in the second column.

(R_2)→1/7*(R_2)

[[1,1,1,0],[0,1,4/7,1/7],[0,−7,−4,−1]]

4. Eliminate the entries above and below the leading 1 in the second column by subtracting the second row from the first row and adding 7 times the second row to the third row.

(R_1)→(R_1)−(R_2)

(R_3)→(R_3)+7*(R_2)

[[1,0,3/7,−1/7],[0,1,4/7,1/7],[0,0,0,0]]

Final Answer

rref*[[2,2,2,0],[−2,5,2,1],[8,1,4,−1]]=[[1,0,3/7,−1/7],[0,1,4/7,1/7],[0,0,0,0]]

Want more problems? Check here!