Find Reduced Row Echelon Form [[1,7,0],[0,1,8],[0,0,1]]

Problem

[[1,7,0],[0,1,8],[0,0,1]]

Solution

1. Identify the current state of the matrix. The matrix is already in row echelon form (REF) because it is upper triangular with ones on the main diagonal.

2. Eliminate the entry in the second row, third column. To create a zero at (R_2),(C_3) perform the row operation (R_2)←(R_2)−8*(R_3)

[[1,7,0],[0,1,0],[0,0,1]]

3. Eliminate the entry in the first row, second column. To create a zero at (R_1),(C_2) perform the row operation (R_1)←(R_1)−7*(R_2)

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

Final Answer

rref*[[1,7,0],[0,1,8],[0,0,1]]=[[1,0,0],[0,1,0],[0,0,1]]

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