Find Reduced Row Echelon Form

Problem

[[4,3,−3,−7],[−8,−3,15,−1],[16,3,−39,17]]

Solution

1. Create a leading one in the first row by multiplying (R_1) by 1/4

[[1,3/4,−3/4,−7/4],[−8,−3,15,−1],[16,3,−39,17]]

2. Eliminate entries below the first pivot by performing (R_2)→(R_2)+8*(R_1) and (R_3)→(R_3)−16*(R_1)

[[1,3/4,−3/4,−7/4],[0,3,9,−15],[0,−9,−27,45]]

3. Create a leading one in the second row by multiplying (R_2) by 1/3

[[1,3/4,−3/4,−7/4],[0,1,3,−5],[0,−9,−27,45]]

4. Eliminate entries above and below the second pivot by performing (R_1)→(R_1)−3/4*(R_2) and (R_3)→(R_3)+9*(R_2)

[[1,0,−3,2],[0,1,3,−5],[0,0,0,0]]

Final Answer

rref*[[4,3,−3,−7],[−8,−3,15,−1],[16,3,−39,17]]=[[1,0,−3,2],[0,1,3,−5],[0,0,0,0]]

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