Find Reduced Row Echelon Form [[1,1,1,180],[1,0,-1,59],[-1,-1,1,8]]

Problem

[[1,1,1,180],[1,0,−1,59],[−1,−1,1,8]]

Solution

1. Eliminate the first entries in the second and third rows by performing row operations (R_2)−(R_1)→(R_2) and (R_3)+(R_1)→(R_3)

[[1,1,1,180],[0,−1,−2,−121],[0,0,2,188]]

2. Normalize the second and third rows by multiplying (R_2) by −1 and (R_3) by 1/2

[[1,1,1,180],[0,1,2,121],[0,0,1,94]]

3. Eliminate the entries above the pivot in the third column by performing (R_2)−2*(R_3)→(R_2) and (R_1)−(R_3)→(R_1)

[[1,1,0,86],[0,1,0,−67],[0,0,1,94]]

4. Eliminate the entry above the pivot in the second column by performing (R_1)−(R_2)→(R_1)

[[1,0,0,153],[0,1,0,−67],[0,0,1,94]]

Final Answer

[[1,1,1,180],[1,0,−1,59],[−1,−1,1,8]]=[[1,0,0,153],[0,1,0,−67],[0,0,1,94]]

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