Find Reduced Row Echelon Form [[5,1,4],[1,0,5],[0,1,1]]

Problem

[[5,1,4],[1,0,5],[0,1,1]]

Solution

1. Swap rows to place a 1 in the top-left position by moving the second row to the first row.

[[1,0,5],[5,1,4],[0,1,1]]

2. Eliminate the first element of the second row by performing the row operation (R_2)−5*(R_1)⇒(R_2)

[[1,0,5],[0,1,−21],[0,1,1]]

3. Eliminate the second element of the third row by performing the row operation (R_3)−(R_2)⇒(R_3)

[[1,0,5],[0,1,−21],[0,0,22]]

4. Normalize the third row by dividing it by 22 to create a leading 1.

[[1,0,5],[0,1,−21],[0,0,1]]

5. Eliminate the third element of the second row by performing the row operation (R_2)+21*(R_3)⇒(R_2)

[[1,0,5],[0,1,0],[0,0,1]]

6. Eliminate the third element of the first row by performing the row operation (R_1)−5*(R_3)⇒(R_1)

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

Final Answer

[[5,1,4],[1,0,5],[0,1,1]]=[[1,0,0],[0,1,0],[0,0,1]]

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