The set U = {(x, y) | xy ≥ 0} is not a subspace of the vector space R². A valid demonstration involves finding vectors u and v within U such that their sum does not belong to U, specifically the example (-3, -1) + (2, 2) = (-1, 1). This example confirms that U fails to meet the criteria for being a subspace, as it does not satisfy all necessary properties, despite being a subset of R².
PREREQUISITESStudents studying linear algebra, mathematicians analyzing vector spaces, and anyone seeking to understand the properties of subspaces in R².
What does "it" refer to? are you trying to show that the sum of two vectors in the set may not be in the set? If so, yes, that is valid.pakkanen said:Homework Statement
Task: Show that U = {(x, y) | xy ≥ 0} is not a subspace of vector space R2
I wish you could help me to understand why U is not a subspace of R2x2.
I have actually found a vectors u and v such that it does not belong to U (e.g. (-3,-1) +(2,2) = (-1,1) )
Well, first, you are not trying to show U is not a subset. It is. But it is not a subspace. I suspect that was a typo. Yes, this is sufficient. To be a subspace, the subset must satisfy a number of properties. If it fails to satisfy anyone of them it is not a subspace.but is that sufficient to show that U is not a subset of R2x2?
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