Find Reduced Row Echelon Form [[1,2,3,4],[4,5,6,7],[6,7,8,9]]

Problem

[[1,2,3,4],[4,5,6,7],[6,7,8,9]]

Solution

1. Eliminate the first entries in the second and third rows by performing row operations (R_2)−4*(R_1)→(R_2) and (R_3)−6*(R_1)→(R_3)

[[1,2,3,4],[0,−3,−6,−9],[0,−5,−10,−15]]

2. Normalize the second row by dividing it by −3 using the operation −1/3*(R_2)→(R_2)

[[1,2,3,4],[0,1,2,3],[0,−5,−10,−15]]

3. Eliminate the entry below the second pivot by performing (R_3)+5*(R_2)→(R_3)

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

4. Eliminate the entry above the second pivot to reach reduced row echelon form by performing (R_1)−2*(R_2)→(R_1)

[[1,0,−1,−2],[0,1,2,3],[0,0,0,0]]

Final Answer

rref*([1,2,3,4],[4,5,6,7],[6,7,8,9])=[[1,0,−1,−2],[0,1,2,3],[0,0,0,0]]

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