Basis for row and column space

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Homework Help Overview

The discussion revolves around determining the basis and dimensions of the row space (RS) and column space (CS) of a given matrix A. The matrix A is presented with specific entries, and participants are exploring the properties of its row space.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are examining whether all non-zero rows of the matrix can serve as a basis for the row space. They discuss the necessary conditions for a set of vectors to be considered a basis, including spanning, linear independence, and membership in the row space.

Discussion Status

The discussion is active, with participants questioning the validity of their assumptions regarding the basis of the row space and the conditions that must be satisfied. There is a focus on clarifying terminology and ensuring understanding of the concepts involved.

Contextual Notes

There is a question about the meaning of "RS," which indicates a potential gap in understanding terminology related to the topic. Participants are also considering the implications of the zero row in the matrix on the dimensions of the spaces discussed.

FourierX
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Homework Statement



Can anyone help me figure out basis for RS(A) and basis for CS (A) along with their dimension?
I mean dim CS(A) and dim RS(A)

where A is
[1 -2 4 1]
[0 7 -15 -4]
[0 0 0 0]


Homework Equations





The Attempt at a Solution



are all non zero rows the basis for RS (A)?
 
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FourierX said:
are all non zero rows the basis for RS (A)?
You tell me? To be a basis, you need three things:
1. Each of the nonzero rows are elements of RS(A)
2. The nonzero rows span RS(A)
3. The nonzero rows are linearly independent.
(Right? This should be familiar...)

Are all of these conditions satisfied?
 
yeah, right. so the dimension of the RS(A) is the number of elements of it, correct?
 
What does "RS" mean?
 
row space
 

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