# What are elementary transformations of a matrix

Publish On: 2019-04-14

Total Post: 819

# Mjay Jollay

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## ANS: What are elementary transformations of a matrix

The following six transformations on a matrix are known as elementary transformations. Three of them are due to rows and three due to columns.

(i) Interchange of any two rows or two columns.

(ii) Multiplication of the elements of any row or column by a non-zero number.

(iii) The addition of some multiple of the elements of any row (or column) to the corresponding elements of another row (or column).

Symbols used for elementary transformations:

(i) Rij denotes the interchange of ith and jth row, whereas Cij denotes the interchange of ith and jth columns.

(ii) Ri(k) stands for the multiplications of the elements of ith row by k, k ≠ 0.

(iii) Rij(k) means that the elements of jth row are multiplied by a number k and then added to the corresponding elements of ith row. Clearly the operation Rij(k) on any given matrix meaning is given to Cij (k).