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

Problem

[[7,2,1,0],[3,7,0,1]]

Solution

1. Normalize the first row by multiplying (R_1) by 1/7 to create a leading 1 in the first column.

(R_1)→1/7*(R_1)

[[1,2/7,1/7,0],[3,7,0,1]]

2. Eliminate the first column entry in the second row by subtracting 3 times (R_1) from (R_2)

(R_2)→(R_2)−3*(R_1)

[[1,2/7,1/7,0],[0,43/7,−3/7,1]]

3. Normalize the second row by multiplying (R_2) by 7/43 to create a leading 1 in the second column.

(R_2)→7/43*(R_2)

[[1,2/7,1/7,0],[0,1,−3/43,7/43]]

4. Eliminate the second column entry in the first row by subtracting 2/7 times (R_2) from (R_1)

(R_1)→(R_1)−2/7*(R_2)

[[1,0,7/43,−2/43],[0,1,−3/43,7/43]]

Final Answer

rref*([7,2,1,0],[3,7,0,1])=[[1,0,7/43,−2/43],[0,1,−3/43,7/43]]

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