Question

How is row and column operations are done

Answer 1

Elementary Matrix Operations Elementary Operations

There are three kinds of elementary matrix operations.

1. Interchange two rows (or columns).
2. Multiply each element in a row (or column) by a non-zero number.
3. Multiply a row (or column) by a non-zero number and add the result to another row (or column).

When these operations are performed on rows, they are called elementary row operations; and when they are performed on columns, they are called elementary column operations.

Elementary Operation Notation

In many references, you will encounter a compact notation to describe elementary operations. That notation is shown below.

Operation description Notation

Row operations
1. Interchange rows i and j	Ri <--> Rj
2. Multiply row i by s, where s ≠ 0	sRi --> Ri
3. Add s times row i to row j	sRi + Rj --> Rj
Column operations
1. Interchange columns iand j	Ci <--> Cj
2. Multiply column i by s, where s ≠ 0	sCi --> Ci
3. Add s times column ito column j	sCi + Cj --> Cj

Elementary Operators

Each type of elementary operation may be performed by matrix multiplication, using square matrices calledelementary 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.

R1 <--> R2 =	0 1 1 0		1 3 5 2 4 6
	E		A

R1 <--> R2 =

0 + 2 0 + 4 0 + 6 0 + 1 0 + 3 0 + 5

R1 <--> R2 =

2 4 6 1 3 5

= B

Here, E is an elementary operator. It operates on A to produce the desired interchanged rows in B. What we would like to know, of course, is how to find E. Read on.