Find Reduced Row Echelon Form [[1,0,1,9],[0,1,0,8],[0,0,-1,6]]

Problem

[[1,0,1,9],[0,1,0,8],[0,0,−1,6]]

Solution

1. Identify the pivot in the third row, which is −1 at position (3,3)

2. Normalize the third row by multiplying (R_3) by −1 to make the pivot a 1

(R_3)→−1⋅(R_3)

[[1,0,1,9],[0,1,0,8],[0,0,1,−6]]

3. Eliminate the entry above the pivot in the third column by subtracting (R_3) from (R_1)

(R_1)→(R_1)−(R_3)

[[1,0,0,15],[0,1,0,8],[0,0,1,−6]]

4. Verify that the matrix is now in reduced row echelon form, as each leading entry is 1 it is the only non-zero entry in its column, and leading entries move to the right as we go down rows.

Final Answer

rref*[[1,0,1,9],[0,1,0,8],[0,0,−1,6]]=[[1,0,0,15],[0,1,0,8],[0,0,1,−6]]

Want more problems? Check here!