Find Reduced Row Echelon Form [[5x+2y=1],[-3x+3y=5]]

Problem

[[5,2,1],[−3,3,5]]

Solution

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

[[5,2,1],[−3,3,5]]

2. Divide the first row (R_1) by 5 to create a leading 1 in the first column.

(R_1)→1/5*(R_1)

[[1,2/5,1/5],[−3,3,5]]

3. Eliminate the xterm in the second row by adding 3 times the first row to the second row.

(R_2)→(R_2)+3*(R_1)

[[1,2/5,1/5],[0,21/5,28/5]]

4. Multiply the second row (R_2) by 5/21 to create a leading 1 in the second column.

(R_2)→5/21*(R_2)

[[1,2/5,1/5],[0,1,4/3]]

5. Eliminate the yterm in the first row by subtracting 2/5 times the second row from the first row.

(R_1)→(R_1)−2/5*(R_2)

[[1,0,−1/3],[0,1,4/3]]

Final Answer

[[5,2,1],[−3,3,5]]=[[1,0,−1/3],[0,1,4/3]]

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