Find Reduced Row Echelon Form [[6,1,5],[9,24,2]]

Problem

[[6,1,5],[9,24,2]]

Solution

1. Divide the first row by 6 to create a leading 1 in the first column.

[[1,1/6,5/6],[9,24,2]]

2. Eliminate the 9 in the second row by subtracting 9 times the first row from the second row ((R_2)⇒(R_2)−9*(R_1).

[[1,1/6,5/6],[0,45/2,−11/2]]

3. Normalize the second row by multiplying it by 2/45 to create a leading 1 in the second column.

[[1,1/6,5/6],[0,1,−11/45]]

4. Eliminate the 1/6 in the first row by subtracting 1/6 times the second row from the first row ((R_1)⇒(R_1)−1/6*(R_2).

[[1,0,5/6−1/6*(−11/45)],[0,1,−11/45]]

5. Simplify the constant in the first row: 5/6+11/270=225/270+11/270=236/270=118/135

[[1,0,118/135],[0,1,−11/45]]

Final Answer

rref*[[6,1,5],[9,24,2]]=[[1,0,118/135],[0,1,−11/45]]

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