# Basis maths-linear algebra-Q5

While Solving the System of linear equations, the three Elementary row operations are as following :

1. Row Interchange : A row within the matrix can be switched with another row.
2. Row Scaling : Each element in a row can be multiplied by a non zero constant.
3. Row Replacement : A row can be replaced by the sum of that row and a multiple of another row.

Which of the following is True regarding Elementary Row operations?

(A). Row Replacement can be implied from other Two elementary row operations.

(B). Row Interchange can be implied from other Two elementary row operations.

(C). Row Scaling can be implied from other Two elementary row operations.

(D). None of the elementary operations can be implied from other Two. asked May 15
reshown May 16

Using Row Scaling and Row replacement, we can do row interchange.

Assume R,S are two rows. And we want to interchange them.

Initially (R,S) ;

Apply Row replacement; (R-S,S);

Apply Row replacement; (R-S, R);

Apply row replacement; (-S,R) ;

Apply row scaling; (S,R)

The motive of this question is to convey that the "elementary" three row operations are Not all "elementary". Using the operations Row Scaling and Row replacement, we can Interchange tow rows. answered May 16 by (112,760 points)
edited May 19
i could not understand it so, plz elaborate it.
i could not understand it so, please elaborate it.
Question is asking that one of these three elementary operations is Not really elementary because using the other two operations we can do what that operation does. In answer, we have shown that "row interchange" can be accomplished using "row replacement and row scaling".