Find Reduced Row Echelon Form [[1,-3,4,7],[0,1,2,2],[0,0,1,5]]

Problem

[[1,−3,4,7],[0,1,2,2],[0,0,1,5]]

Solution

1. Identify the pivot in the third row, which is the 1 in the third column. Use this pivot to eliminate the entries above it in the third column.

2. Eliminate the entry in the second row, third column by performing the row operation (R_2)→(R_2)−2*(R_3)

[[1,−3,4,7],[0,1,0,−8],[0,0,1,5]]

3. Eliminate the entry in the first row, third column by performing the row operation (R_1)→(R_1)−4*(R_3)

[[1,−3,0,−13],[0,1,0,−8],[0,0,1,5]]

4. Identify the pivot in the second row, which is the 1 in the second column. Use this pivot to eliminate the entry above it in the second column.

5. Eliminate the entry in the first row, second column by performing the row operation (R_1)→(R_1)+3*(R_2)

[[1,0,0,−37],[0,1,0,−8],[0,0,1,5]]

Final Answer

rref*([1,−3,4,7],[0,1,2,2],[0,0,1,5])=[[1,0,0,−37],[0,1,0,−8],[0,0,1,5]]

Want more problems? Check here!