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

Problem

[[7,2,2],[2,2,7]]

Solution

1. Divide the first row by 7 to create a leading 1 in the first column.

[[1,2/7,2/7],[2,2,7]]

2. Eliminate the 2 in the second row by subtracting 2 times the first row from the second row ((R_2)⇒(R_2)−2*(R_1).

[[1,2/7,2/7],[0,10/7,45/7]]

3. Normalize the second row by multiplying it by 7/10 to create a leading 1 in the second column.

[[1,2/7,2/7],[0,1,9/2]]

4. Eliminate the 2/7 in the first row by subtracting 2/7 times the second row from the first row ((R_1)⇒(R_1)−2/7*(R_2).

[[1,0,−1],[0,1,9/2]]

Final Answer

[[7,2,2],[2,2,7]]=[[1,0,−1],[0,1,9/2]]

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