Simplify the Matrix [[1,0,1,0],[1,1,1,1],[2,-1,2,-1]]

Problem

[[1,0,1,0],[1,1,1,1],[2,−1,2,−1]]

Solution

1. Identify the goal to simplify the matrix into its Reduced Row Echelon Form (RREF) using elementary row operations.

2. Eliminate the first entry of the second row by performing the operation (R_2)−(R_1)→(R_2)

[[1,0,1,0],[0,1,0,1],[2,−1,2,−1]]

3. Eliminate the first entry of the third row by performing the operation (R_3)−2*(R_1)→(R_3)

[[1,0,1,0],[0,1,0,1],[0,−1,0,−1]]

4. Eliminate the second entry of the third row by performing the operation (R_3)+(R_2)→(R_3)

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

Final Answer

[[1,0,1,0],[1,1,1,1],[2,−1,2,−1]]=[[1,0,1,0],[0,1,0,1],[0,0,0,0]]

Want more problems? Check here!