Question

Elementary Operations On Matrix

Answer 1

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.

(i) The interchange of any two rows or two columns:

Symbolically the interchange of i^th and j^th rows is denoted by R_i ↔ R_j and interchange of i^th and j^th column is denoted bY C_i ↔ C_j

(ii) The multiplication of the elements of any row or column by a non zero number : Symbolically, the multiplication of each element of the i^th row by k, where k ≠ 0 is denoted by R_i → k R_i.

The corresponding column operation is denoted by C_j → kC_j

(iii) The addition to the elements of any row or colum, the corresponding elements of any other row or column multiplied by any non zero number : Symbolically, the addition to the elements of i^th row, the corresponding elements of j^th row multiplied by k is denoted by R_i → R_i + kR_j

The corresponding column operation is denoted by C_i → C_i + kC_j