Find Reduced Row Echelon Form [[1000,5000,10000,99000],[2,1,0,26]]

Problem

[[1000,5000,10000,99000],[2,1,0,26]]

Solution

1. Divide the first row by 1000 to create a leading 1 in the first column.

[[1,5,10,99],[2,1,0,26]]

2. Eliminate the 2 in the second row by subtracting 2 times the first row from the second row ((R_2)←(R_2)−2*(R_1).

[[1,5,10,99],[0,−9,−20,−172]]

3. Divide the second row by −9 to create a leading 1 in the second column.

[[1,5,10,99],[0,1,20/9,172/9]]

4. Eliminate the 5 in the first row by subtracting 5 times the second row from the first row ((R_1)←(R_1)−5*(R_2).

(R_1)←1−5*(0)=1

(R_1)←5−5*(1)=0

(R_1)←10−5*(20/9)=90/9−100/9=−10/9

(R_1)←99−5*(172/9)=891/9−860/9=31/9

5. Construct the final reduced row echelon form matrix.

[[1,0,−10/9,31/9],[0,1,20/9,172/9]]

Final Answer

[[1000,5000,10000,99000],[2,1,0,26]]=[[1,0,−10/9,31/9],[0,1,20/9,172/9]]

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