Find Reduced Row Echelon Form [[6,-8,10],[-3/4,1,-5/4]]

Problem

[[6,−8,10],[−3/4,1,−5/4]]

Solution

1. Normalize the first row by multiplying (R_1) by 1/6 to create a leading 1 in the first column.

1/6*(R_1)→(R_1)

[[1,−4/3,5/3],[−3/4,1,−5/4]]

2. Eliminate the first entry of the second row by adding 3/4 times (R_1) to (R_2)

(R_2)+3/4*(R_1)→(R_2)

[[1,−4/3,5/3],[0,0,0]]

3. Identify that the matrix is now in reduced row echelon form because the leading entry of the first row is 1 it is the only non-zero entry in its column, and the second row consists entirely of zeros.

Final Answer

rref*[[6,−8,10],[−3/4,1,−5/4]]=[[1,−4/3,5/3],[0,0,0]]

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