Find Reduced Row Echelon Form [[-6,7],[2,6],[-4,1]]

Problem

[[−6,7],[2,6],[−4,1]]

Solution

1. Swap rows to place a smaller, more manageable number in the first row's pivot position. Swap (R_1) and (R_2)

[[2,6],[−6,7],[−4,1]]

2. Normalize the first row by multiplying (R_1) by 1/2 to create a leading 1.

[[1,3],[−6,7],[−4,1]]

3. Eliminate entries below the first pivot by performing the row operations (R_2)→(R_2)+6*(R_1) and (R_3)→(R_3)+4*(R_1)

[[1,3],[0,25],[0,13]]

4. Normalize the second row by multiplying (R_2) by 1/25 to create the second leading 1.

[[1,3],[0,1],[0,13]]

5. Eliminate entries above and below the second pivot by performing the row operations (R_1)→(R_1)−3*(R_2) and (R_3)→(R_3)−13*(R_2)

[[1,0],[0,1],[0,0]]

Final Answer

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

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