Vector Subspaces: Determining U as a Subspace of M4x4 Matrices

mathiebug7
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Determine whether the following subsets U of M4x4is a subspace of the vector space V of all M4x4 matrices, with
the standard operations of matrix addition and scalar multiplication. If is not a subspace provide an example to
demonstrate a property that U does not possess.
a. The set U of all 4x4 upper symmetric matrices
 
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What are upper symmetric matrices? Doesn't sound symmetric though. And what do you think? You should show us your work!
 
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mathiebug7 said:
a. The set U of all 4x4 upper symmetric matrices
I am familiar with "upper triangular" and "symmetric", but I don't know what "upper symmetric" is.

In any case, you should proceed step-by-step through the definition of a vector space and show whether or not each requirement is satisfied. If any of them are difficult, we can give hints and guidance on textbook-type problems where you show your work.
 
fresh_42 said:
What are upper symmetric matrices? Doesn't sound symmetric though. And what do you think?
I'm guessing diagonal matrices. :wink:
 
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vela said:
I'm guessing diagonal matrices. :wink:
This could be a way out if there wasn't that "U" and the extensive description of how to find a counterexample. Very suspicious, Watson!
 
fresh_42 said:
This could be a way out if there wasn't that "U" and the extensive description of how to find a counterexample. Very suspicious, Watson!
The OP seems to have posed only the (a) part of the question. Presumably the b, c, etc parts have been left out …
 
vela said:
I'm guessing diagonal matrices. :wink:
That certainly would work. This gets my vote.
 
Ultimately, OP needs to show operational closure under addition, scaling.
 
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WWGD said:
Ultimately, OP needs to show operational closure under addition, scaling.
Good point. IMO, for a beginning student, it would be good for him to go down the properties and list the ones that are inherited. Then prove the closure properties that are not just inherited.
 
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