Find Reduced Row Echelon Form [[1,2],[2,4],[3,6]]

Problem

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

Solution

1. Identify the first pivot in the first row, which is already 1 at position (1,1)

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

[[1,2],[2−2*(1),4−2*(2)],[3,6]]=[[1,2],[0,0],[3,6]]

3. Eliminate the entry in the third row by performing the row operation (R_3)−3*(R_1)→(R_3)

[[1,2],[0,0],[3−3*(1),6−3*(2)]]=[[1,2],[0,0],[0,0]]

4. Verify that the matrix is now in reduced row echelon form, as the first non-zero entry in the first row is 1 it is the only non-zero entry in its column, and all zero rows are at the bottom.

Final Answer

rref*[[1,2],[2,4],[3,6]]=[[1,2],[0,0],[0,0]]

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