Elementary transformations of a matrix, Equivalent Matrices

**Elementary Transformations and Equivalent
matrices**

(i) Interchange of any two rows (or columns): *R _{i}*
â†”

(ii) Multiplication of each element of a row (or
column) by any non-zero scalar *k *:* R _{i} *â†’

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

*R _{i} *â†’

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 *B *~ *A *.

Tags : Rank of a Matrix , 12th Business Maths and Statistics : Chapter 1 : Applications of Matrices and Determinants

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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

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