Find Reduced Row Echelon Form [[2x+7y=48],[3x-12y=27]]

Problem

[[2,7,48],[3,−12,27]]

Solution

1. Write the system as an augmented matrix.

[[2,7,48],[3,−12,27]]

2. Divide the second row by 3 to simplify the coefficients.

(R_2)→1/3*(R_2)

[[2,7,48],[1,−4,9]]

3. Swap the first and second rows to get a 1 in the top-left position.

(R_1)↔(R_2)

[[1,−4,9],[2,7,48]]

4. Eliminate the xterm in the second row by subtracting 2 times the first row from the second row.

(R_2)→(R_2)−2*(R_1)

[[1,−4,9],[0,15,30]]

5. Divide the second row by 15 to get a leading 1 in the second row.

(R_2)→1/15*(R_2)

[[1,−4,9],[0,1,2]]

6. Eliminate the yterm in the first row by adding 4 times the second row to the first row.

(R_1)→(R_1)+4*(R_2)

[[1,0,17],[0,1,2]]

Final Answer

[[2,7,48],[3,−12,27]]=[[1,0,17],[0,1,2]]

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