Is the Equation Ax=w Consistent for A in M4,3 and w as v1+v2?

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Homework Help Overview

The discussion revolves around the consistency of the equation Ax = w, where A is a 4x3 matrix and w is defined as the sum of two vectors v1 and v2 in R^4. The original poster attempts to establish a relationship between the matrix A and the vectors through the equation, seeking to prove consistency in the context of linear transformations.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants explore the relationship between the matrix A and the vectors v1 and v2, questioning how to express the sum of the transformations. There is an inquiry into rewriting the equation in a different form, specifically considering the implications of combining the vectors u1 and u2.

Discussion Status

The discussion is ongoing, with participants engaging in exploratory reasoning about the mathematical relationships involved. Some guidance has been offered regarding rewriting the equation, but there is no explicit consensus on the correctness of the initial approach or the next steps to take.

Contextual Notes

Participants express uncertainty about the correctness of their initial attempts and the overall setup of the problem. There is a focus on ensuring that the transformations and their implications are properly understood, without resolving the underlying questions.

ykaire
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1. Let A∈ Μ4,3
(that is, a 4 x 3 matrix). Let v1, v2 ∈ R^4 and let w = v1 +v2. Suppose there exists u1, u2 as an element of R^3 such that v1 = Au1 and v2= Au2
prove the Ax=w is consistent

Homework Equations


3.i honestly don't know if I'm doing this correctly at all, but this is what I have done so far:
Ax=w where A is a 4x3 matrix.
Ax=v1 + v2
Ax=Au1 + Au2
then i don't know what to do.
 
Last edited:
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ykaire said:
1. Let A∈ Μ4,3
(that is, a 4 x 3 matrix). Let v1, v2 ∈ R^4 and let w = v1 +v2. Suppose there exists u1, u2 as an element of R^3 such that v1 = Au1 and v2= Au2
prove the Ax=w is consistent

Homework Equations


3.i honestly don't know if I'm doing this correctly at all, but this is what I have done so far:
Ax=w where A is a 4x3 matrix.
Ax=v1 + v2
Ax=Au1 + Au2
then i don't know what to do.

Well, can you write Au_1 + Au_2 another way?
 
jbunniii said:
Well, can you write Au_1 + Au_2 another way?

I guess I could write the equation as

x= u1 + u2

but, like i said, i don't even know if i even started the problem off correctly.
 
Well, what is Ax= A(u1+ u2)?
 
HallsofIvy said:
Well, what is Ax= A(u1+ u2)?

it reduces to x= u1 + u2
 

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