Find Reduced Row Echelon Form

Problem

[[1,−4,−6,−1,7,0],[0,0,1,1,−8,0],[0,0,0,0,2,0],[0,0,0,0,0,0]]

Solution

1. Identify the pivot in the third row, which is the value 2 in the fifth column.

2. Normalize the third row by multiplying (R_3) by 1/2 to create a leading 1

[[1,−4,−6,−1,7,0],[0,0,1,1,−8,0],[0,0,0,0,1,0],[0,0,0,0,0,0]]

3. Eliminate the entries above the pivot in the fifth column by performing row operations (R_2)⇒(R_2)+8*(R_3) and (R_1)⇒(R_1)−7*(R_3)

[[1,−4,−6,−1,0,0],[0,0,1,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,0]]

4. Identify the pivot in the second row, which is the value 1 in the third column.

5. Eliminate the entry above this pivot in the first row by performing the row operation (R_1)⇒(R_1)+6*(R_2)

[[1,−4,0,5,0,0],[0,0,1,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,0]]

Final Answer

rref*[[1,−4,−6,−1,7,0],[0,0,1,1,−8,0],[0,0,0,0,2,0],[0,0,0,0,0,0]]=[[1,−4,0,5,0,0],[0,0,1,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,0]]

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