Simplify the Matrix

Problem

[[0,1,2,3],[1,1,0,0],[0,1,1,1],[1,0,0,0]]

Solution

1. Swap rows to place a leading 1 in the first column of the first row. Swap (R_1) and (R_4)

[[1,0,0,0],[1,1,0,0],[0,1,1,1],[0,1,2,3]]

2. Eliminate the entry in the second row, first column by performing (R_2)−(R_1)→(R_2)

[[1,0,0,0],[0,1,0,0],[0,1,1,1],[0,1,2,3]]

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

[[1,0,0,0],[0,1,0,0],[0,0,1,1],[0,1,2,3]]

4. Eliminate the entry in the fourth row, second column by performing (R_4)−(R_2)→(R_4)

[[1,0,0,0],[0,1,0,0],[0,0,1,1],[0,0,2,3]]

5. Eliminate the entry in the fourth row, third column by performing (R_4)−2*(R_3)→(R_4)

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

6. Eliminate the entry in the third row, fourth column by performing (R_3)−(R_4)→(R_3) to reach Reduced Row Echelon Form.

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

Final Answer

[[0,1,2,3],[1,1,0,0],[0,1,1,1],[1,0,0,0]]=[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]

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