Find Reduced Row Echelon Form [[-3,-2],[4,4],[5,7]]

Problem

[[−3,−2],[4,4],[5,7]]

Solution

1. Normalize the first row by multiplying row 1 ((R_1) by −1/3 to create a leading 1.

[[1,2/3],[4,4],[5,7]]

2. Eliminate the first column entries below the leading 1 by performing the row operations (R_2)⇒(R_2)−4*(R_1) and (R_3)⇒(R_3)−5*(R_1)

[[1,2/3],[0,4/3],[0,11/3]]

3. Normalize the second row by multiplying (R_2) by 3/4 to create the next leading 1.

[[1,2/3],[0,1],[0,11/3]]

4. Eliminate the second column entries above and below the leading 1 by performing (R_1)⇒(R_1)−2/3*(R_2) and (R_3)⇒(R_3)−11/3*(R_2)

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

Final Answer

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

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