Finding a Solution for a System of Equations with Given Vectors

Click For Summary

Homework Help Overview

The discussion revolves around finding a system of equations for which a given set of vectors serves as solutions. The vectors in question are (1,0,1), (2,-1,0), (0,-1,-2), and (1,1,3). The subject area pertains to linear algebra and systems of equations.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore methods to formulate a system of equations based on the provided vectors. There are attempts to express the vectors in terms of a linear combination and questions regarding the correctness of equalizing each component to zero. Some participants express uncertainty about the nature of the system of equations and whether it can accommodate multiple solution vectors.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and questioning the validity of their approaches. Some guidance has been offered regarding equalizing components to zero, but there is no consensus on the correct interpretation of the problem or the formulation of the equations.

Contextual Notes

There is uncertainty about whether the problem involves a system of linear equations that can have multiple solutions or if it is asking for a set of equations where each vector is a solution independently. This ambiguity affects the direction of the discussion.

transgalactic
Messages
1,386
Reaction score
0
find an equation system for which these vectors is it solutions

(1,0,1)
(2,-1,0)
(0,-1,-2)
(1,1,3)

i tried:
i can guess (x+2y+0*z+t,0*x -y-z+t,x+0-2*z +3*t)=x(1,0,1) +y(2,-1,0) +z(0,-1,-2)+t(1,1,3)

but what i got is a big vector
how i get the equations?
 
Physics news on Phys.org
i was told to equalize each part to zero
x+2y+0*z+t=0
etc..

is it correct??
i can't understand why its correct?
 
How does one usually go about solving a system of Linear equations to find the solution vectors?

It represents (In some equivalent row or column form) a matrix equation Ax=y, with x and y vectors.

Are you sure this is a system of linear equations? Because if it is, then you aren't going to have four different solution vectors, ever, for one system of linear equations. So all you should have to do is write a set of dependent equations.

Unless the question is as I suspect, find a set of linear equations such that each of these vectors independently is a solution.
 
Last edited:
i was told to equalize each part to zero
x+2y+0*z+t=0

etc..
is it correct??
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
Replies
8
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K
Replies
6
Views
1K
Replies
7
Views
2K