Find Reduced Row Echelon Form [[1,5,-6],[1,6,5],[2,8,7]]

Problem

[[1,5,−6],[1,6,5],[2,8,7]]

Solution

1. Identify the first pivot in the first column, which is already 1 at (R_1)

2. Eliminate the entries below the first pivot by performing row operations (R_2)→(R_2)−(R_1) and (R_3)→(R_3)−2*(R_1)

[[1,5,−6],[0,1,11],[0,−2,19]]

3. Identify the second pivot in the second column, which is 1 at (R_2)

4. Eliminate the entries above and below the second pivot by performing (R_1)→(R_1)−5*(R_2) and (R_3)→(R_3)+2*(R_2)

[[1,0,−61],[0,1,11],[0,0,41]]

5. Normalize the third row to create the third pivot by performing (R_3)→1/41*(R_3)

[[1,0,−61],[0,1,11],[0,0,1]]

6. Eliminate the entries above the third pivot by performing (R_1)→(R_1)+61*(R_3) and (R_2)→(R_2)−11*(R_3)

[[1,0,0],[0,1,0],[0,0,1]]

Final Answer

[[1,5,−6],[1,6,5],[2,8,7]]=[[1,0,0],[0,1,0],[0,0,1]]

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