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# Elementary Transformations and Equivalent matrices

Elementary transformations of a matrix, Equivalent Matrices

Elementary Transformations and Equivalent matrices

## Elementary transformations of a matrix

(i) Interchange of any two rows (or columns): Ri â†” R j (or Ci â†”Cj ) .

(ii) Multiplication of each element of a row (or column) by any non-zero scalar k : Ri â†’ kRi (or Ci â†’kCi )

(iii) Addition to the elements of any row (or column) the same scalar multiples of corresponding elements of any other row (or column):

Ri â†’ Ri +kRj .(or Ci â†’ Ci + kCj )

## Equivalent Matrices

Two matrices A and B are said to be equivalent if one is obtained from the another by applying a finite number of elementary transformations and we write it as A ~ B or A .

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12th Business Maths and Statistics : Chapter 1 : Applications of Matrices and Determinants : Elementary Transformations and Equivalent matrices | Rank of a Matrix