Find Reduced Row Echelon Form

Problem

[[1,1.61,0.35,564.2],[1,0.2,0.8,428],[3.67,3.86,0.8,1610.9]]

Solution

1. Eliminate the first entry in the second row by subtracting the first row from the second row ((R_2)−(R_1)→(R_2).

[[1,1.61,0.35,564.2],[0,−1.41,0.45,−136.2],[3.67,3.86,0.8,1610.9]]

2. Eliminate the first entry in the third row by subtracting 3.67 times the first row from the third row ((R_3)−3.67*(R_1)→(R_3).

[[1,1.61,0.35,564.2],[0,−1.41,0.45,−136.2],[0,−2.0487,−0.4845,−459.714]]

3. Normalize the second row by dividing it by −1.41 to create a leading one ((R_2)/−1.41→(R_2).

[[1,1.61,0.35,564.2],[0,1,−0.3191489,96.5957447],[0,−2.0487,−0.4845,−459.714]]

4. Eliminate the second entry in the third row by adding 2.0487 times the second row to the third row ((R_3)+2.0487*(R_2)→(R_3).

[[1,1.61,0.35,564.2],[0,1,−0.3191489,96.5957447],[0,0,−1.1383404,−261.8183]]

5. Normalize the third row by dividing it by −1.1383404 to create a leading one ((R_3)/−1.1383404→(R_3).

[[1,1.61,0.35,564.2],[0,1,−0.3191489,96.5957447],[0,0,1,230]]

6. Eliminate the third entries in the first and second rows using the third row ((R_2)+0.3191489*(R_3)→(R_2) and (R_1)−0.35*(R_3)→(R_1).

[[1,1.61,0,483.7],[0,1,0,170],[0,0,1,230]]

7. Eliminate the second entry in the first row by subtracting 1.61 times the second row from the first row ((R_1)−1.61*(R_2)→(R_1).

[[1,0,0,210],[0,1,0,170],[0,0,1,230]]

Final Answer

rref*[[1,1.61,0.35,564.2],[1,0.2,0.8,428],[3.67,3.86,0.8,1610.9]]=[[1,0,0,210],[0,1,0,170],[0,0,1,230]]

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