Find Reduced Row Echelon Form [[1,3,6],[1,4,5]]

Problem

[[1,3,6],[1,4,5]]

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_1)→(R_2)

[[1,3,6],[1−1,4−3,5−6]]

[[1,3,6],[0,1,−1]]

3. Identify the second pivot in the second row, which is 1 at position (2,2)

4. Eliminate the entry above the second pivot to create a zero at position (1,2) by performing the row operation (R_1)−3*(R_2)→(R_1)

[[1−3*(0),3−3*(1),6−3*(−1)],[0,1,−1]]

[[1,0,9],[0,1,−1]]

Final Answer

rref*[[1,3,6],[1,4,5]]=[[1,0,9],[0,1,−1]]

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