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

[matqkks]

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.

 

[DonAntonio]

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

 

[CAF123]

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.

 

[Stephen Tashi]

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.