Find Reduced Row Echelon Form [[5x+8y=21],[-9x-7y=14]]

Problem

[[5,8,21],[−9,−7,14]]

Solution

1. Normalize the first row by multiplying (R_1) by 1/5 to create a leading 1 in the first column.

(R_1)←1/5*(R_1)

[[1,8/5,21/5],[−9,−7,14]]

2. Eliminate the first column entry in the second row by adding 9 times (R_1) to (R_2)

(R_2)←(R_2)+9*(R_1)

[[1,8/5,21/5],[0,37/5,259/5]]

3. Normalize the second row by multiplying (R_2) by 5/37 to create a leading 1 in the second column.

(R_2)←5/37*(R_2)

[[1,8/5,21/5],[0,1,7]]

4. Eliminate the second column entry in the first row by subtracting 8/5 times (R_2) from (R_1)

(R_1)←(R_1)−8/5*(R_2)

[[1,0,−7],[0,1,7]]

Final Answer

[[5,8,21],[−9,−7,14]]=[[1,0,−7],[0,1,7]]

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