Find Reduced Row Echelon Form [[1,2,-9,-8],[0,1,7,-3],[0,0,1,7]]

Problem

[[1,2,−9,−8],[0,1,7,−3],[0,0,1,7]]

Solution

1. Identify the pivot in the third row, which is the 1 in the third column.

2. Eliminate the entries above the third-row pivot by performing row operations on the second and first rows.

3. Apply the row operation (R_2)→(R_2)−7*(R_3) to clear the entry in the second row, third column.

(R_2)→[0,1,7,−3]−7*[0,0,1,7]=[0,1,0,−52]

[[1,2,−9,−8],[0,1,0,−52],[0,0,1,7]]

4. Apply the row operation (R_1)→(R_1)+9*(R_3) to clear the entry in the first row, third column.

(R_1)→[1,2,−9,−8]+9*[0,0,1,7]=[1,2,0,55]

[[1,2,0,55],[0,1,0,−52],[0,0,1,7]]

5. Identify the pivot in the second row, which is the 1 in the second column.

6. Eliminate the entry above the second-row pivot by applying the row operation (R_1)→(R_1)−2*(R_2)

(R_1)→[1,2,0,55]−2*[0,1,0,−52]=[1,0,0,159]

[[1,0,0,159],[0,1,0,−52],[0,0,1,7]]

Final Answer

[[1,2,−9,−8],[0,1,7,−3],[0,0,1,7]]=[[1,0,0,159],[0,1,0,−52],[0,0,1,7]]

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