Finding the Image of a Line for Beginners

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Homework Help Overview

The discussion revolves around finding the image of a line in the context of linear transformations. The original poster expresses difficulty with a specific problem that lacks examples in the textbook.

Discussion Character

  • Exploratory, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need to express variables in terms of others and the challenges posed by the lack of examples in the textbook. There is mention of using matrix form and inverses, but the original poster is unsure how to proceed with only one equation.

Discussion Status

Some participants have provided expressions for the variables involved, and there is a suggestion to substitute these into the line equation to find the image. The conversation indicates a progression in understanding, although the original poster's frustration with the textbook's lack of clarity remains evident.

Contextual Notes

The original poster notes that the textbook does not provide examples for the specific case they are working on, which contributes to their confusion. There is also a reference to the need for two equations in the context of the problem.

Octavius1287
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Im stuck on this, the book has no examples on this kind of problem (and its the first one) And i learn mostly from examples

Im on b) and i can't figure out gow to get the image of the line
the back says the answer should be 9y1-4y2=6 and I've spent over a hour on this and I am not seeing it
IMG_20130320_115711_145_zps48df21c6.jpg
 
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The first step is to find an expression for x1 and x2 in terms of y1 and y2.
 
the book shows how to do that but only with 2 equation and putting them in matrix form then getting the inverse, i only have 1 equation. For this case its not explained and no example is given
 
Octavius1287 said:
the book shows how to do that but only with 2 equation and putting them in matrix form then getting the inverse, i only have 1 equation.

I mean do it with the equations defining the linear transformation. There are two of those.
 
ok i got
x1=(3/2)y1-(1/2)y2

x2=-2y1+y2
 
Octavius1287 said:
ok i got
x1=(3/2)y1-(1/2)y2

x2=-2y1+y2

Great! Now substitute those into the line equation. That will give you the image of the line.
 
oooh ok thanks. why can't the book just say that!
 

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