Find Reduced Row Echelon Form [[1,-5,-6,-1],[-4,13,10,-3]]

Problem

[[1,−5,−6,−1],[−4,13,10,−3]]

Solution

1. Identify the first pivot in the first row, which is already 1 in the first column.

2. Eliminate the entry below the first pivot by adding 4 times the first row to the second row ((R_2)←(R_2)+4*(R_1).

(R_2):[−4+4*(1),13+4*(−5),10+4*(−6),−3+4*(−1)]

(R_2):[0,−7,−14,−7]

[[1,−5,−6,−1],[0,−7,−14,−7]]

3. Normalize the second row by dividing it by −7 to create a pivot of 1 ((R_2)←−1/7*(R_2).

(R_2):[0,1,2,1]

[[1,−5,−6,−1],[0,1,2,1]]

4. Eliminate the entry above the second pivot by adding 5 times the second row to the first row ((R_1)←(R_1)+5*(R_2).

(R_1):[1+5*(0),−5+5*(1),−6+5*(2),−1+5*(1)]

(R_1):[1,0,4,4]

[[1,0,4,4],[0,1,2,1]]

Final Answer

[[1,−5,−6,−1],[−4,13,10,−3]]=[[1,0,4,4],[0,1,2,1]]

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