Find Reduced Row Echelon Form [[2,6,27],[3,5,53]]

Problem

[[2,6,27],[3,5,53]]

Solution

1. Create a leading one in the first row by multiplying (R_1) by 1/2

1/2*(R_1)→(R_1)

[[1,3,27/2],[3,5,53]]

2. Eliminate the first entry of the second row by subtracting 3 times (R_1) from (R_2)

(R_2)−3*(R_1)→(R_2)

[[1,3,27/2],[0,−4,25/2]]

3. Create a leading one in the second row by multiplying (R_2) by −1/4

−1/4*(R_2)→(R_2)

[[1,3,27/2],[0,1,−25/8]]

4. Eliminate the second entry of the first row by subtracting 3 times (R_2) from (R_1)

(R_1)−3*(R_2)→(R_1)

[[1,0,183/8],[0,1,−25/8]]

Final Answer

[[2,6,27],[3,5,53]]=[[1,0,183/8],[0,1,−25/8]]

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