Find Reduced Row Echelon Form [[1,0,1,0],[0,1,0,0],[1,0,1,0]]

Problem

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

Solution

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

2. Eliminate the entry below the first pivot by performing the row operation (R_3)−(R_1)→(R_3)

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

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

3. Identify the second pivot in the second row, which is the 1 in the second column.

4. Check for further operations. Since all entries below the second pivot are already zero and there are no entries above it in its column to clear, the matrix is now in reduced row echelon form.

Final Answer

rref*[[1,0,1,0],[0,1,0,0],[1,0,1,0]]=[[1,0,1,0],[0,1,0,0],[0,0,0,0]]

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