Find Reduced Row Echelon Form [[12,-15,9],[-2,3,4],[8,-10,6]]

Problem

[[12,−15,9],[−2,3,4],[8,−10,6]]

Solution

1. Divide the first row (R_1) by 12 to create a leading 1 in the first column.

[[1,−1.25,0.75],[−2,3,4],[8,−10,6]]

2. Eliminate the first column entries below the leading 1 by performing (R_2)+2*(R_1)⇒(R_2) and (R_3)−8*(R_1)⇒(R_3)

[[1,−1.25,0.75],[0,0.5,5.5],[0,0,0]]

3. Divide the second row (R_2) by 0.5 to create a leading 1 in the second column.

[[1,−1.25,0.75],[0,1,11],[0,0,0]]

4. Eliminate the entry above the leading 1 in the second column by performing (R_1)+1.25*(R_2)⇒(R_1)

[[1,0,14.5],[0,1,11],[0,0,0]]

Final Answer

rref*[[12,−15,9],[−2,3,4],[8,−10,6]]=[[1,0,29/2],[0,1,11],[0,0,0]]

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