Find Reduced Row Echelon Form [[-3,-3,9],[4,1,-18],[2,-1,-12]]

Problem

[[−3,−3,9],[4,1,−18],[2,−1,−12]]

Solution

1. Divide the first row by −3 to create a leading 1 in the first column.

[[1,1,−3],[4,1,−18],[2,−1,−12]]

2. Eliminate the entries below the leading 1 in the first column by performing (R_2)−4*(R_1)⇒(R_2) and (R_3)−2*(R_1)⇒(R_3)

[[1,1,−3],[0,−3,−6],[0,−3,−6]]

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

[[1,1,−3],[0,1,2],[0,−3,−6]]

4. Eliminate the entries above and below the leading 1 in the second column by performing (R_1)−(R_2)⇒(R_1) and (R_3)+3*(R_2)⇒(R_3)

[[1,0,−5],[0,1,2],[0,0,0]]

Final Answer

rref*[[−3,−3,9],[4,1,−18],[2,−1,−12]]=[[1,0,−5],[0,1,2],[0,0,0]]

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