Find Reduced Row Echelon Form [[1,1,0,1,-2],[1,-1,0,-1,2]]

Problem

[[1,1,0,1,−2],[1,−1,0,−1,2]]

Solution

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

2. Eliminate the entry below the first pivot by performing the row operation (R_2)−(R_1)→(R_2)

[[1,1,0,1,−2],[0,−2,0,−2,4]]

3. Normalize the second row to create a leading 1 by dividing (R_2) by −2 which is the operation −1/2*(R_2)→(R_2)

[[1,1,0,1,−2],[0,1,0,1,−2]]

4. Eliminate the entry above the second pivot by performing the row operation (R_1)−(R_2)→(R_1)

[[1,0,0,0,0],[0,1,0,1,−2]]

Final Answer

rref*[[1,1,0,1,−2],[1,−1,0,−1,2]]=[[1,0,0,0,0],[0,1,0,1,−2]]

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