Find Reduced Row Echelon Form [[0,0,3,0],[100000,40000,18000,254000]]

Problem

[[0,0,3,0],[100000,40000,18000,254000]]

Solution

1. Swap rows to place the row with the leading non-zero entry at the top.

[[100000,40000,18000,254000],[0,0,3,0]]

2. Divide the first row by 100000 to create a leading 1 in the first column.

[[1,0.4,0.18,2.54],[0,0,3,0]]

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

[[1,0.4,0.18,2.54],[0,0,1,0]]

4. Eliminate the entry above the leading 1 in the third column by performing (R_1)←(R_1)−0.18*(R_2)

[[1,0.4,0,2.54],[0,0,1,0]]

Final Answer

rref*([0,0,3,0],[100000,40000,18000,254000])=[[1,0.4,0,2.54],[0,0,1,0]]

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