HSC Science (Electronics) 12th Board ExamMaharashtra State Board
Share
Notifications

View all notifications

Elementary Operation (Transformation) of a Matrix

Login
Create free account


      Forgot password?

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 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)]`
Video link : https://youtu.be/tvGi0suZW2U

Video Tutorials

We have provided more than 1 series of video tutorials for some topics to help you get a better understanding of the topic.

Series 1


Series 2


Shaalaa.com | Elementary row transformation

Shaalaa.com


Next video


Shaalaa.com


Elementary row transformation [00:32:29]
S
Series 1: playing of 2
1
0%


Related QuestionsVIEW ALL [8]

S
View in app×