Mathematics Asked by Neothehero on December 21, 2020

- Why we called the three actions of row operation "elementary"? Is there a thing called "advanced" or "complicated" row operation?
- I’ve seen the word "non-elementary" row operation is used to describe things like $R_1-R_2$, which is not written in the conventional $-1R_2 + R_1$. Is this usage correct? In particular, what should $R_1-R_2$ be called?

begin{align*}

&text{a) A non-elementary row operation} \

&text{b) An elementary row operation} \

&text{c) Just a row operation} \

&text{d) It is not a row operation}

end{align*}

The sense of "elementary" here is that all the operations that preserve the row-space of a matrix can be be produced by combining various elementary row operations.

Thus these are the *elementary* steps that can be taken to calculate a (reduced) row echelon form of a matrix, a basic tool for solving several kinds of problems involving the row-space of a matrix and the solutions (if any) of a linear system of equations.

With regard to what $R_1 - R_2$ ought to be called, something is missing from the description. It would indeed be an elementary row operation if this "new row" immediately replaces $R_1$. If you wanted it to replace $R_2$, you would have to perform that row operation by combining two "elementary row operation" steps (first replace $R_2$ with $R_2 - R_1$, then multiply the resulting new second row by non-zero scalar $-1$).

If you wanted to do something completely different with $R_1 - R_2$, then it would possibly either not be a row operation or not a row operation that preserved the row space of the matrix. For example, if you replaced $R_3$ with $R_1 - R_2$ (leaving $R_1,R_2$ as they are), you might well be making the row space of the matrix *smaller*.

Correct answer by hardmath on December 21, 2020

2 Asked on December 20, 2020 by akash-jain

1 Asked on December 20, 2020 by liz

2 Asked on December 20, 2020

diagonalization eigenvalues eigenvectors linear algebra linear transformations matrices

1 Asked on December 20, 2020 by sunit-das

3 Asked on December 20, 2020 by chunky-norris

2 Asked on December 20, 2020 by user842445

0 Asked on December 20, 2020 by masmath

1 Asked on December 20, 2020 by ispring-quiz

1 Asked on December 19, 2020 by latus_rectum

2 Asked on December 19, 2020 by grompchompz

1 Asked on December 19, 2020 by enock-kabibi

4 Asked on December 19, 2020 by shiran-shaharabani

1 Asked on December 19, 2020 by xuuserac

2 Asked on December 19, 2020 by akash-karnatak

0 Asked on December 19, 2020 by isak

1 Asked on December 19, 2020 by stakmod

compactness convergence divergence metric spaces real analysis sequences and series

2 Asked on December 19, 2020 by perfectoid

2 Asked on December 18, 2020 by sammy

0 Asked on December 18, 2020 by peng-yu

Get help from others!

Recent Questions

Recent Answers

- haakon.io on Why fry rice before boiling?
- Peter Machado on Why fry rice before boiling?
- Joshua Engel on Why fry rice before boiling?
- Lex on Does Google Analytics track 404 page responses as valid page views?
- Jon Church on Why fry rice before boiling?

© 2022 AnswerBun.com. All rights reserved. Sites we Love: PCI Database, MenuIva, UKBizDB, Menu Kuliner, Sharing RPP