Are there any real life applications of the rank of a matrix? It need

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Discussion Overview

The discussion centers around the real-life applications of the rank of a matrix, particularly in motivating students to learn about this concept in mathematics. Participants explore various contexts where matrix rank may be relevant, including theoretical and practical implications.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions the necessity of real-life applications to motivate students, suggesting that mathematics is valuable for developing logical thinking and rational deduction, rather than solely for practical applications.
  • Another participant proposes that airports utilize linear systems, where the rank of matrices can provide insights into nullity and invertibility, although they are unsure of everyday applications of matrix rank.
  • A different viewpoint highlights that the rank of a matrix relates to the dimension of the image in transformations, which could be relevant for students interested in computer graphics and video games.

Areas of Agreement / Disagreement

Participants express differing opinions on the importance of real-life applications for motivating students. While some argue for the necessity of practical relevance, others emphasize the intrinsic value of mathematics beyond its applications.

Contextual Notes

Participants do not reach a consensus on the necessity of real-life applications for learning about matrix rank, and the discussion includes various assumptions about the role of mathematics in education.

matqkks
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Are there any real life applications of the rank of a matrix? It need to have a real impact which motivates students why they should learn about rank.
 
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matqkks said:
Are there any real life applications of the rank of a matrix? It need to have a real impact which motivates students why they should learn about rank.


As many applications to "real life" of trigonometric functions, logarithms and derivatives: you shalln't be

using this stuff any time you go to the grocery store, to take a bus or even to cash a check in the bank.

By this time it should be well understood that studying maths is way beyond its "real life" (what is that, anyway?)

applications on "normal" people's lives. It is about thinking logically, deducing correctly stuff, having some

mental processes in a way we'd call rational, etc.

DonAntonio
 


I believe a 'real life' application to solving linear systems is in airports. A substantial number of equations are solved via high technical computers, which encodes information about passengers, flights etc..With regard to rank, in terms of using this information when solving a linear system, you could extract information about its nullity, whether it is invertible and other things, as detailed in various linear algebra theorems. I don't know of any everyday uses of the rank of a matrix.

However, I would disagree about your comment about 'needing a real impact which motivates students'. Many students will study mathematics for its 'beauty, power and ubiquity' as one of my professors put it.
 


If we view a square matrix as specifying a transformation, the rank tells you about the dimension of the image. For example a 3x3 matrix that maps 3D space onto a 2D plane is one that won''t have "full rank". Students interested in the mathematics of computer graphics and video games might be interested in that. Computer graphics can be used to motivate many topics in linear algebra.
 

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