ERO

1. ELEMENTARY ROW
OPERATIONS (ERO)
BY SANAULLAH MEMON

2. ELEMENTARY ROW OPERATIONS (ERO)

3. Row Equivalent
Matrices A≈B
ONE CAN BE OBTAINED FROM THE OTHER BY PERFORMING A FINITE
SEQUENCE OF ELEMENTARY ROW OPERATIONS.

4. EXAMPLES
 𝐴 =
1 5 2 3
3 1 8 −1
2 5 1 6
3 R2
 𝐵 =
1 5 2 3
9 3 24 −3
2 5 1 6
 “matrix B is Row Equivalent to matrix A” and write 𝐵 ≈ 𝐴.

5. we interchange R1 and R3 of matrix
A, (denoted by R13)
 𝐴 =
1 5 2 3
3 1 8 −1
2 5 1 6
R13
𝐶 =
2 5 1 6
3 1 8 −1
1 5 2 3 “matrix C is Row Equivalent to matrix
A” and write𝐶 ≈ 𝐴.

6. R1 is multiplied by say 4 and the result is added into
R2, (denoted by R2 + 4 R1),
𝐴 =
1 5 2 3
3 1 8 −1
2 5 1 6
R2 + 4 R1
𝐷 =
1 5 2 3
7 21 16 11
2 5 1 6
“matrix D is Row Equivalent to matrix
A” and write. 𝐷 ≈ 𝐴

7. THE END
This Photo by Unknown Author is licensed under CC BY-SA-NC