Find Reduced Row Echelon Form [[3x-y=5],[4x+2y=0]]

Problem

[[3,−1,5],[4,2,0]]

Solution

1. Write the augmented matrix representing the system of linear equations.

[[3,−1,5],[4,2,0]]

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

(R_2)→1/2*(R_2)

[[3,−1,5],[2,1,0]]

3. Add the second row to the first row to eliminate the −1 in the first row.

(R_1)→(R_1)+(R_2)

[[5,0,5],[2,1,0]]

4. Divide the first row by 5 to create a leading 1

(R_1)→1/5*(R_1)

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

5. Subtract 2 times the first row from the second row to eliminate the 2 in the second row.

(R_2)→(R_2)−2*(R_1)

[[1,0,1],[0,1,−2]]

Final Answer

[[3,−1,5],[4,2,0]]→[[1,0,1],[0,1,−2]]

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