Linear algebra

[babadany2999]

I'm having trouble understanding the exercise done in the book.Suppose U={(x,x,y,y) belonging to F4 : x,y belong to F} 6 ^ W = {(x,x,x,y) belonging to F4 : x,y belong to F}
In the book it says U+V = {(x,x,y,z) belonging to F4 : x,y,z belong to F} .I'm having trouble understanding this,where did the z come from,shouldn't we have on the 4th position y? And in the third why is x+y=y?Thanks for the help!

 

[Otis]

… U={(x,x,y,y) belonging to F4 : x,y belong to F} 6 ^ W = {(x,x,x,y) belonging to F4 : x,y belong to F}

Hi babadany. Can you post an image of what you're looking at?

… U+V

Have they defined V?

… in the third why is x+y=y?

I don't see x+y.

\(\;\)

 

[babadany2999]

Hi babadany. Can you post an image of what you're looking at?


Have they defined V?


I don't see x+y.

Hi,bad wording on my part,i meant U+W.
Here is a picture

 

[HallsofIvy]

I'm having trouble understanding the exercise done in the book.Suppose U={(x,x,y,y) belonging to F4 : x,y belong to F} 6 ^ W = {(x,x,x,y) belonging to F4 : x,y belong to F}
In the book it says U+V = {(x,x,y,z) belonging to F4 : x,y,z belong to F} .I'm having trouble understanding this,where did the z come from,shouldn't we have on the 4th position y? And in the third why is x+y=y?Thanks for the help!

One "complication" is that you are using "x" and "y" to represent different thing in different places. I would write U= {(a, a, b, b)} and W= {(c, c, c d)}. Then U+ W= {a+ c, a+ c, b+ c, b+ d} The first two components are the same, a+ c, so call that "x". Since a, b, c and d can be any numbers, so b+ c and b+ d are not necessarily related- call them "y" and "z".

That is why they say U+ W (NOT "U+ V" there is no "V" in this problem) is {x, x, y z}.