Find Reduced Row Echelon Form [[3,-2,4,0],[9,-6,12,0],[6,-4,8,0]]

Problem

[[3,−2,4,0],[9,−6,12,0],[6,−4,8,0]]

Solution

1. Normalize the first row by dividing (R_1) by 3 to create a leading 1

1/3*(R_1)→(R_1)

[[1,−2/3,4/3,0],[9,−6,12,0],[6,−4,8,0]]

2. Eliminate the first entry of the second row by subtracting 9 times (R_1) from (R_2)

(R_2)−9*(R_1)→(R_2)

[[1,−2/3,4/3,0],[0,0,0,0],[6,−4,8,0]]

3. Eliminate the first entry of the third row by subtracting 6 times (R_1) from (R_3)

(R_3)−6*(R_1)→(R_3)

[[1,−2/3,4/3,0],[0,0,0,0],[0,0,0,0]]

4. Verify the matrix is in reduced row echelon form, as the leading entry of the first row is 1 and all other rows are zero.

Final Answer

[[3,−2,4,0],[9,−6,12,0],[6,−4,8,0]]=[[1,−2/3,4/3,0],[0,0,0,0],[0,0,0,0]]

Want more problems? Check here!