- #1
Saladsamurai
- 3,020
- 7
This is an example that I am a little confused by:
[tex]U={(x,0,0)\in\mathbf{F}^3:x\in\mathbf{F}}\text{ and }W={(0,y,0)\in\mathbf{F}^3:y\in\mathbf{F}}[/tex]
Then
[tex]U+W={(x,y,0):x,y\in\mathbf{F}[/tex]
Okay, I get that. Now it says that U is defined the same as above but now let
[tex]W={(y,y,0)\in\mathbf{F}^3:y\in\mathbf{F}}[/tex]
Then the sum of U and W is the same as given above. Why is that? What is happening to that y that is in the "x" position?Perhaps I am confusing the definition of the sum of two lists with the sum of two subspaces.
[tex]U={(x,0,0)\in\mathbf{F}^3:x\in\mathbf{F}}\text{ and }W={(0,y,0)\in\mathbf{F}^3:y\in\mathbf{F}}[/tex]
Then
[tex]U+W={(x,y,0):x,y\in\mathbf{F}[/tex]
Okay, I get that. Now it says that U is defined the same as above but now let
[tex]W={(y,y,0)\in\mathbf{F}^3:y\in\mathbf{F}}[/tex]
Then the sum of U and W is the same as given above. Why is that? What is happening to that y that is in the "x" position?Perhaps I am confusing the definition of the sum of two lists with the sum of two subspaces.
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