Find Reduced Row Echelon Form [[10,15000],[7,94000],[5,54000]]

Problem

[[10,15000],[7,94000],[5,54000]]

Solution

1. Divide the first row by 10 to create a leading 1 in the first column.

[[1,1500],[7,94000],[5,54000]]

2. Eliminate the entries below the leading 1 in the first column by performing (R_2)−7*(R_1)⇒(R_2) and (R_3)−5*(R_1)⇒(R_3)

[[1,1500],[0,83500],[0,46500]]

3. Divide the second row by 83500 to create a leading 1 in the second column.

[[1,1500],[0,1],[0,46500]]

4. Eliminate the entries above and below the leading 1 in the second column by performing (R_1)−1500*(R_2)⇒(R_1) and (R_3)−46500*(R_2)⇒(R_3)

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

Final Answer

rref*[[10,15000],[7,94000],[5,54000]]=[[1,0],[0,1],[0,0]]

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