Find Reduced Row Echelon Form [[2,5,8],[-1,0,-1/4],[3,4,27/4]]

Problem

[[2,5,8],[−1,0,−1/4],[3,4,27/4]]

Solution

1. Swap the first and second rows to get a leading coefficient of −1 in the top left, then multiply the new first row by −1 to create a leading 1

[[1,0,1/4],[2,5,8],[3,4,27/4]]

2. Eliminate the entries below the leading 1 in the first column by performing (R_2)−2*(R_1)→(R_2) and (R_3)−3*(R_1)→(R_3)

[[1,0,1/4],[0,5,15/2],[0,4,6]]

3. Normalize the second row by multiplying (R_2) by 1/5 to create a leading 1 in the second column.

[[1,0,1/4],[0,1,3/2],[0,4,6]]

4. Eliminate the entry below the leading 1 in the second column by performing (R_3)−4*(R_2)→(R_3)

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

Final Answer

rref*[[2,5,8],[−1,0,−1/4],[3,4,27/4]]=[[1,0,1/4],[0,1,3/2],[0,0,0]]

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