Find Reduced Row Echelon Form [[2x+y=6],[2x+5y=22]]

Problem

{[2*x+y=6],[2*x+5*y=22])

Solution

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

[[2,1,6],[2,5,22]]

2. Create a zero in the first column of the second row by subtracting the first row from the second row ((R_2)−(R_1)⇒(R_2).

[[2,1,6],[0,4,16]]

3. Normalize the second row by dividing it by 4 to create a leading 1 ((R_2)/4⇒(R_2).

[[2,1,6],[0,1,4]]

4. Create a zero in the second column of the first row by subtracting the second row from the first row ((R_1)−(R_2)⇒(R_1).

[[2,0,2],[0,1,4]]

5. Normalize the first row by dividing it by 2 to create a leading 1 ((R_1)/2⇒(R_1).

[[1,0,1],[0,1,4]]

Final Answer

RREF*[[2,1,6],[2,5,22]]=[[1,0,1],[0,1,4]]

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