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

Problem

[[1,2],[2,−2]]

Solution

1. Identify the first pivot in the first row, which is already 1 at position (1,1)

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

[[1,2],[2−2*(1),−2−2*(2)]]

[[1,2],[0,−6]]

3. Normalize the second row to create a pivot of 1 at position (2,2) by performing (R_2)⇒−1/6*(R_2)

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

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

[[1−2*(0),2−2*(1)],[0,1]]

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

Final Answer

rref*([1,2],[2,−2])=[[1,0],[0,1]]

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