Find Reduced Row Echelon Form [[-1,2,4],[-6,6,24]]

Problem

[[−1,2,4],[−6,6,24]]

Solution

1. Normalize the first row by multiplying (R_1) by −1 to create a leading 1 in the first column.

(R_1)→−1⋅(R_1)

[[1,−2,−4],[−6,6,24]]

2. Eliminate the first column entry in the second row by adding 6 times (R_1) to (R_2)

(R_2)→(R_2)+6*(R_1)

[[1,−2,−4],[0,−6,0]]

3. Normalize the second row by multiplying (R_2) by −1/6 to create a leading 1 in the second column.

(R_2)→−1/6⋅(R_2)

[[1,−2,−4],[0,1,0]]

4. Eliminate the second column entry in the first row by adding 2 times (R_2) to (R_1) to reach reduced row echelon form.

(R_1)→(R_1)+2*(R_2)

[[1,0,−4],[0,1,0]]

Final Answer

rref*[[−1,2,4],[−6,6,24]]=[[1,0,−4],[0,1,0]]

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