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 by`C_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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Shaalaa.com | Elementary row transformation
The sum of three numbers is 9. If we multiply third number by 3 and add to the second number, we get 16. By adding the first and the third number and then subtracting twice the second number from this sum, we get 6. Use this information and find the system of linear equations. Hence, find the three numbers using matrices.
The cost of 2 books, 6 notebooks and 3 pens is Rs 40. The cost of 3 books, 4 notebooks and 2 pens is Rs 35, while the cost of 5 books, 7 notebooks and 4 pens is Rs 61. Using this information and matrix method, find the cost of 1 book, 1 notebook and 1 pen separately.
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