Find Reduced Row Echelon Form [[4,5,8],[8,10,-3]]

Problem

[[4,5,8],[8,10,−3]]

Solution

1. Divide the first row (R_1) by 4 to create a leading 1 in the first column.

[[1,5/4,2],[8,10,−3]]

2. Eliminate the entry in the first column of the second row by performing the row operation (R_2)−8*(R_1)→(R_2)

[[1,5/4,2],[0,0,−19]]

3. Divide the second row (R_2) by −19 to create a leading 1 in the third column.

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

4. Eliminate the entry in the third column of the first row by performing the row operation (R_1)−2*(R_2)→(R_1)

[[1,5/4,0],[0,0,1]]

Final Answer

rref*[[4,5,8],[8,10,−3]]=[[1,5/4,0],[0,0,1]]

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