Find Reduced Row Echelon Form [[3,-2,0],[6,-4,-8],[1,12,-2]]

Problem

[[3,−2,0],[6,−4,−8],[1,12,−2]]

Solution

1. Swap rows to place a 1 in the first pivot position by moving the third row to the first row.

[[1,12,−2],[6,−4,−8],[3,−2,0]]

2. Eliminate the entries below the first pivot by performing (R_2)−6*(R_1)→(R_2) and (R_3)−3*(R_1)→(R_3)

[[1,12,−2],[0,−76,4],[0,−38,6]]

3. Scale the second row by dividing by −76 to create a leading 1

[[1,12,−2],[0,1,−1/19],[0,−38,6]]

4. Eliminate the entries above and below the second pivot by performing (R_1)−12*(R_2)→(R_1) and (R_3)+38*(R_2)→(R_3)

[[1,0,−26/19],[0,1,−1/19],[0,0,4]]

5. Scale the third row by dividing by 4 to create the final leading 1

[[1,0,−26/19],[0,1,−1/19],[0,0,1]]

6. Eliminate the entries above the third pivot by performing (R_1)+26/19*(R_3)→(R_1) and (R_2)+1/19*(R_3)→(R_2)

[[1,0,0],[0,1,0],[0,0,1]]

Final Answer

rref*[[3,−2,0],[6,−4,−8],[1,12,−2]]=[[1,0,0],[0,1,0],[0,0,1]]

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