Find Reduced Row Echelon Form [[6,-8,5],[-9,12,7]]

Problem

[[6,−8,5],[−9,12,7]]

Solution

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

[[1,−4/3,5/6],[−9,12,7]]

2. Eliminate the first entry of the second row by adding 9 times the first row to the second row.

(R_2)⇒(R_2)+9*(R_1)

[[1,−4/3,5/6],[0,0,29/2]]

3. Normalize the second row by multiplying it by 2/29 to create a leading 1 in the second row.

(R_2)⇒2/29*(R_2)

[[1,−4/3,5/6],[0,0,1]]

4. Eliminate the entry above the leading 1 in the third column by subtracting 5/6 times the second row from the first row.

(R_1)⇒(R_1)−5/6*(R_2)

[[1,−4/3,0],[0,0,1]]

Final Answer

rref*([6,−8,5],[−9,12,7])=[[1,−4/3,0],[0,0,1]]

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