This document contains a summary of elementary row operations on matrices by Sunipa Bera. It introduces the three types of elementary row operations: interchanging rows, multiplying a row by a scalar, and adding a scalar multiple of one row to another. It explains that each operation can be performed by premultiplying the matrix by a elementary operator matrix derived from applying the operation to the identity matrix. Examples are provided to illustrate how to obtain the elementary operator matrix and use it to perform each type of elementary row operation on a given matrix.

1. SUNIPA BERA
B.TECH CSE(CSF)
ROLL NO:. 2

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4. Elementary Operations

5. Operation description Notation
Row Operations
1. Interchange rows i and j Ri <_>Rj
2. Multiply row i by s, where s≠0 sRi  Rj
3. Add s times row i to row j sRi + Rj = Rj
Column Operations
1. Interchange column i and j Ci<—>Cj
2. Multiply column i by s, where s≠0 sCiCj
3.Add s times column i to column j sCi+CjCj

6. Elementary Operation
Each type of elementary operation may be performed by matrix multiplication, using square matrices called elementary operators.
For example, suppose you want to interchange rows 1 and 2 of matrix A. To accomplish this, you could premultiply A by E to produce
B, as shown below.

7. How to Perform Elementary Row Operations
To perform an elementary row operation on a A, an r x c matrix, take the following steps.
To find E, the elementary row operator, apply the operation to an r x r identity matrix.
To carry out the elementary row operation, pre multiply A by E.
We illustrate this process below for each of the three types of elementary row operations.

8. Interchange two rows.

9. Multiply a row by a number.

10. Multiply a row and add it to another row.

11. identity matrix

13. - guided by Naveen Sir