Find Reduced Row Echelon Form [[1,2,0,0],[3,4,0,0]]

Problem

[[1,2,0,0],[3,4,0,0]]

Solution

1. Identify the first pivot in the first row, which is already 1 in the first column.

2. Eliminate the entry below the first pivot by performing the row operation (R_2)⇒(R_2)−3*(R_1)

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

[[1,2,0,0],[0,−2,0,0]]

3. Normalize the second row to create a pivot of 1 by performing the row operation (R_2)⇒−1/2*(R_2)

[[1,2,0,0],[0,1,0,0]]

4. Eliminate the entry above the second pivot by performing the row operation (R_1)⇒(R_1)−2*(R_2)

[[1−2*(0),2−2*(1),0−2*(0),0−2*(0)],[0,1,0,0]]

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

Final Answer

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

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