Find Reduced Row Echelon Form [[4,4,8,0],[-12,-12,-24,0],[0,-3,-9,0]]

Problem

[[4,4,8,0],[−12,−12,−24,0],[0,−3,−9,0]]

Solution

1. Divide the first row (R_1) by 4 to create a leading 1 in the first column.

[[1,1,2,0],[−12,−12,−24,0],[0,−3,−9,0]]

2. Eliminate the entry in the second row, first column by adding 12 times (R_1) to (R_2)

[[1,1,2,0],[0,0,0,0],[0,−3,−9,0]]

3. Swap the second row (R_2) and the third row (R_3) to move the non-zero row up.

[[1,1,2,0],[0,−3,−9,0],[0,0,0,0]]

4. Divide the second row (R_2) by −3 to create a leading 1 in the second column.

[[1,1,2,0],[0,1,3,0],[0,0,0,0]]

5. Eliminate the entry in the first row, second column by subtracting (R_2) from (R_1)

[[1,0,−1,0],[0,1,3,0],[0,0,0,0]]

Final Answer

rref*[[4,4,8,0],[−12,−12,−24,0],[0,−3,−9,0]]=[[1,0,−1,0],[0,1,3,0],[0,0,0,0]]

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