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

Problem

[[1,2,−3],[2,−1,4],[4,3,−2]]

Solution

1. Eliminate the first entries in the second and third rows by performing row operations (R_2)−2*(R_1)→(R_2) and (R_3)−4*(R_1)→(R_3)

[[1,2,−3],[0,−5,10],[0,−5,10]]

2. Normalize the second row by dividing by −5 using the operation −1/5*(R_2)→(R_2)

[[1,2,−3],[0,1,−2],[0,−5,10]]

3. Eliminate the second entry in the third row by performing the operation (R_3)+5*(R_2)→(R_3)

[[1,2,−3],[0,1,−2],[0,0,0]]

4. Eliminate the entry above the leading 1 in the second column by performing the operation (R_1)−2*(R_2)→(R_1)

[[1,0,1],[0,1,−2],[0,0,0]]

Final Answer

[[1,2,−3],[2,−1,4],[4,3,−2]]=[[1,0,1],[0,1,−2],[0,0,0]]

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