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# Elementary Operation (Transformation) of a Matrix

#### notes

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 ith and jth rows is denoted by R_i ↔ R_j and interchange of i^(th) and j^(th) column is denoted by C_i ↔ C_j.

For example, applying R_1 ↔ R_2 to
A = [(1,2,1),(-1,sqrt3,1),(5,6,7)] ,

we get  [(-1,sqrt3,1),(1,2,1),(5,6,7)]

(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 → kR_i.
The corresponding column  operation is denoted by C_i → kC_i
For example, applying C_3 -> 1/7 C_3 , to B = [(1,2,1),(-1,sqrt3,1)], we get [(1,2,1/7),(-1,sqrt3,1/7)]

(iii) The addition to the elements of any row or column, 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 byC_i → C_i + kC_j.
For example, applying  R_2 → R_2 – 2R_1, to C = [(1,2),(2,-1)], we get [(1,2),(0,-5)]

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Elementary row transformation [00:32:29]
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