MHB Introduction to linear algebra

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The discussion centers on proving that u(z+zw) equals the set {+1, -1, +w, -w, +w^2, -w^2}. Participants express skepticism about the proof's validity, likening it to absurd hypothetical scenarios. There is a call for clarification regarding the definition of "u" in the context of the problem. The conversation highlights the need for more information to approach the proof effectively. Overall, the participants seek a deeper understanding of the mathematical concepts involved.
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prove that u(z+zw)={+1,-1,+w,-w,+w^2,-w^2}
 
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abs said:
prove that u(z+zw)={+1,-1,+w,-w,+w^2,-w^2}

You may as well ask us to prove that if the sky is green then faeces smell like roses...
 
Prove It said:
You may as well ask us to prove that if the sky is green then faeces smell like roses...

If the sky is green, then a storm is coming.
If the storm comes, many things will be blown away, including faeces and roses. This, in turn, makes their smells mixed up.

Sorry, couldn't resist.
 
abs said:
prove that u(z+zw)={+1,-1,+w,-w,+w^2,-w^2}
Seriously, there must be more to this problem. What are you told about "u"?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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