By constructing a counterexample, show that the union of two subspaces is not in general, a subspace?
I don't really have a clue on how to start this. I really only want a hint on how to start his
your question as posed is strange. you usually use counter examples to disprove something, while here it seems like you want to prove something. check the wording and ask again.
as for the hint: begin at the beginning, haha. What does it mean to be a subspace? and in what context are you describing subspaces?
Not a "proof", but yes, as a counter-example, it works. provided you have the definition for addition in given.
I was thinking of an example along the lines of:
= the set of all 2x2 matrices over the reals of the form
and = the set of all 2x2 matrices over the reals of the form
Both with standard matrix addition and scalar multiplication operations.
yes
i mean, at some point in your class or your text it should be written that you can add two coordinates in by adding their corresponding components. refrain from taking an intuitive definition if you can, not unless you know it works (by proving it does, or if your text says so and proves it)--it doesn't always.What do you mean when you say "provided you have the definition for addition in given".