Find Reduced Row Echelon Form [[2,0,-2],[-3,5,28],[4,1,1],[1,-2,-11]]

Problem

[[2,0,−2],[−3,5,28],[4,1,1],[1,−2,−11]]

Solution

1. Swap rows to place a 1 in the first pivot position by moving the fourth row to the top.

[[1,−2,−11],[−3,5,28],[4,1,1],[2,0,−2]]

2. Eliminate the entries below the first pivot by performing (R_2)+3*(R_1) (R_3)−4*(R_1) and (R_4)−2*(R_1)

[[1,−2,−11],[0,−1,−5],[0,9,45],[0,4,20]]

3. Normalize the second row by multiplying (R_2) by −1 to create a leading 1

[[1,−2,−11],[0,1,5],[0,9,45],[0,4,20]]

4. Eliminate the entries above and below the second pivot by performing (R_1)+2*(R_2) (R_3)−9*(R_2) and (R_4)−4*(R_2)

[[1,0,−1],[0,1,5],[0,0,0],[0,0,0]]

Final Answer

rref*[[2,0,−2],[−3,5,28],[4,1,1],[1,−2,−11]]=[[1,0,−1],[0,1,5],[0,0,0],[0,0,0]]

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