Inverse matrix word problem, matrix arithmetic

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Homework Help Overview

The discussion revolves around a word problem involving inverse matrices and matrix arithmetic. The original poster is attempting to set up a matrix based on the problem statement but is struggling with the inversion process and obtaining correct values for variables x, y, and z.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster questions the correctness of their matrix setup and expresses difficulty in inverting the matrix, mentioning the emergence of "inconvenient" numbers. Some participants inquire about the nature of these numbers and suggest that the arithmetic challenges should not deter progress.

Discussion Status

Participants are actively engaging with the original poster's setup, with some confirming the correctness of the matrix while others offer suggestions for handling the arithmetic difficulties. There is a recognition of the challenges faced, but no explicit consensus on a solution has been reached yet.

Contextual Notes

There is a note regarding the posting of images, indicating that participants should type out problems and solutions instead of relying on thumbnails, which may not be accessible to all users.

IrinaK.
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Homework Statement


Hello!
Please, take a look at the attached picture - there is a quote of the exercise and below is my attempt to make a matrix. Is my matrix correct? I have tried many times to convert it to inverse one, but I can't figure out how to do it - I keep getting "inconvenient" numbers that do not further lead to correct answers for x, y and z.

Thank you!

Homework Equations

The Attempt at a Solution

 

Attachments

  • Screen Shot 2014-09-28 at 12.51.33 PM.png
    Screen Shot 2014-09-28 at 12.51.33 PM.png
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IrinaK. said:

Homework Statement


Hello!
Please, take a look at the attached picture - there is a quote of the exercise and below is my attempt to make a matrix. Is my matrix correct? I have tried many times to convert it to inverse one, but I can't figure out how to do it - I keep getting "inconvenient" numbers that do not further lead to correct answers for x, y and z.

Thank you!

Homework Equations

The Attempt at a Solution


Do not post thumbnails; they cannot be read on some media. Just type out the problem and your solution work; it should not take long and is not much trouble.
 
Your set up is correct. Do you not know how to invert a matrix, say, by "row operations"? You say you get "inconvenient numbers". Do you mean just awkward fractions? The fact that the arithmetic is hard shouldn't stop you. If nothing else, you can use decimal arithmetic on a calculator, rounding to, say, three or four decimal places.
 
Thank you :) Yes, you are right. It seems that I always miss a correct digit here and there. Here is what I came up with (without the last row completed)
 

Attachments

  • Screen Shot 2014-09-28 at 5.16.55 PM.png
    Screen Shot 2014-09-28 at 5.16.55 PM.png
    70.1 KB · Views: 679
Ray Vickson said:
Do not post thumbnails; they cannot be read on some media. Just type out the problem and your solution work; it should not take long and is not much trouble.
Actually, it was a rather big picture. Sorry about that.
 

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