Elementary matrix operations play an important role in many matrix algebra applications, such as finding the inverse of a matrix and solving simultaneous linear equations.

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.

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.

Interchange two rows (or columns)

Suppose we wan to interchange the rows and coloums, simply we can interchange the rows are coloums. We denote R1 R2 R3 . . . . Rn and coloums as C1 C2 C3 . . . . . . . . . . Cn

For Example we have a matrix P

Untitled-1 copy1. Interchanging Rows and Columns 

Now Let us do the operation of interchanging C1 with C2 and R1 with R2. after, it will look like this 🙂 This is nothing but Row and Column transformations

Untitled-1 cnopy
Elementary Row and column operations

Let us do a Simple Example

Consider a Matrix P as matrix-operations-homework-help copy

And see the below Operations on both Row and Columns

  • R1<-> R3
  • R2<-> R3
  • R1<->R2
  • C1<->C3
  • C4<->C3
  • C2<->C4
Untitled-b3
After the certain Row and Column operations

 

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