Find Reduced Row Echelon Form [[1,2,3],[4,5,6],[7,8,9]]

Problem

[[1,2,3],[4,5,6],[7,8,9]]

Solution

1. Eliminate the first entries in the second and third rows by subtracting multiples of the first row.

(R_2)←(R_2)−4*(R_1)

(R_3)←(R_3)−7*(R_1)

[[1,2,3],[0,−3,−6],[0,−6,−12]]

2. Normalize the second row by dividing by the leading coefficient.

(R_2)←−1/3*(R_2)

[[1,2,3],[0,1,2],[0,−6,−12]]

3. Eliminate the entries above and below the leading 1 in the second column.

(R_1)←(R_1)−2*(R_2)

(R_3)←(R_3)+6*(R_2)

[[1,0,−1],[0,1,2],[0,0,0]]

Final Answer

rref*[[1,2,3],[4,5,6],[7,8,9]]=[[1,0,−1],[0,1,2],[0,0,0]]

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