Elementary transformation of matrices.
In order to transform a matrix into a specific required form, some operations are done, known as elementary operations or transformation of matrices. There are six operations (transformations) on a matrix, three of which are due to rows and three due to columns, which are known as elementary operations or transformations.
The operations (transformations) on a matrix:
- Interchanging two rows, multiplication a row by either a nonzero value. Denoted by or i.e. interchange of row or column respectively.
Perform the operation which interchange rows on :
- The addition to the elements of any row or column, the corresponding elements of any other row or column are multiplied by any non-zero number. denoted by i.e.the multiplication of each element of the row by k, where k ≠ 0. i.e. the addition to the elements of row, the corresponding elements of row multiplied by
Let us consider a matrix :
Perform the operation on :
- The multiplication of the elements of any row or column by a non-zero number. Denoted by or i.e..the multiplication of each element of the row by , where
Let us consider a matrix :
Perform the operation on