Find Reduced Row Echelon Form [[-8,1,4,-3],[2,1,-1,-3]]

Problem

[[−8,1,4,−3],[2,1,−1,−3]]

Solution

1. Swap rows to place a smaller leading coefficient in the first row for easier calculation.

[[2,1,−1,−3],[−8,1,4,−3]]

2. Eliminate the first entry of the second row by adding 4 times the first row to the second row ((R_2)←(R_2)+4*(R_1).

[[2,1,−1,−3],[0,5,0,−15]]

3. Normalize the second row by dividing it by 5 ((R_2)←1/5*(R_2).

[[2,1,−1,−3],[0,1,0,−3]]

4. Eliminate the entry above the second pivot by subtracting the second row from the first row ((R_1)←(R_1)−(R_2).

[[2,0,−1,0],[0,1,0,−3]]

5. Normalize the first row by dividing it by 2 ((R_1)←1/2*(R_1) to achieve the leading 1.

[[1,0,−1/2,0],[0,1,0,−3]]

Final Answer

[[−8,1,4,−3],[2,1,−1,−3]]=[[1,0,−1/2,0],[0,1,0,−3]]

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