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

Problem

[[1,2,7],[2,1,8]]

Solution

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

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

[[1,2,7],[2−2*(1),1−2*(2),8−2*(7)]]

[[1,2,7],[0,−3,−6]]

3. Normalize the second row to create the second pivot by performing the row operation −1/3*(R_2)⇒(R_2)

[[1,2,7],[0,1,2]]

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

[[1−2*(0),2−2*(1),7−2*(2)],[0,1,2]]

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

Final Answer

[[1,2,7],[2,1,8]]=[[1,0,3],[0,1,2]]

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