Find Reduced Row Echelon Form [[1,-3,5,-2],[2,-1,5,6]]

Problem

[[1,−3,5,−2],[2,−1,5,6]]

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)→(R_2)−2*(R_1)

[[1,−3,5,−2],[2−2*(1),−1−2*(−3),5−2*(5),6−2*(−2)]]

[[1,−3,5,−2],[0,5,−5,10]]

3. Normalize the second row to create the second pivot by performing the row operation (R_2)→1/5*(R_2)

[[1,−3,5,−2],[0,1,−1,2]]

4. Eliminate the entry above the second pivot to reach reduced row echelon form by performing the row operation (R_1)→(R_1)+3*(R_2)

[[1+3*(0),−3+3*(1),5+3*(−1),−2+3*(2)],[0,1,−1,2]]

[[1,0,2,4],[0,1,−1,2]]

Final Answer

[[1,−3,5,−2],[2,−1,5,6]]=[[1,0,2,4],[0,1,−1,2]]

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