Find Reduced Row Echelon Form [[3,3,9,0],[5,6,6,0],[2,5,4,0]]

Problem

[[3,3,9,0],[5,6,6,0],[2,5,4,0]]

Solution

1. Divide the first row by 3 to create a leading 1 in the first column.

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

2. Eliminate the first column entries below the leading 1 by performing (R_2)−5*(R_1)⇒(R_2) and (R_3)−2*(R_1)⇒(R_3)

[[1,1,3,0],[0,1,−9,0],[0,3,−2,0]]

3. Eliminate the second column entries above and below the leading 1 in the second row by performing (R_1)−(R_2)⇒(R_1) and (R_3)−3*(R_2)⇒(R_3)

[[1,0,12,0],[0,1,−9,0],[0,0,25,0]]

4. Divide the third row by 25 to create a leading 1 in the third column.

[[1,0,12,0],[0,1,−9,0],[0,0,1,0]]

5. Eliminate the third column entries above the leading 1 by performing (R_1)−12*(R_3)⇒(R_1) and (R_2)+9*(R_3)⇒(R_2)

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

Final Answer

[[3,3,9,0],[5,6,6,0],[2,5,4,0]]=[[1,0,0,0],[0,1,0,0],[0,0,1,0]]

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