Vector spaces | Mathematics | Page 1

worldly relic Oct 20, 2023, 2:20 AM

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Hi! I’m having trouble proving whether these are vector spaces. I know that in order for a set to be a vector space, it needs to satisfy all ten axioms of the definition of a vector space. These problems are all addition, so I’m not sure how to prove them for scalar multiplication. Please help!

warm pondBOT Oct 20, 2023, 2:20 AM

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worldly relic Hi! I’m having trouble proving whether these are vector spaces. I know that in o...

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zenith crescent Oct 20, 2023, 4:06 AM

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worldly relic Hi! I’m having trouble proving whether these are vector spaces. I know that in o...

You could also prove that these are subspaces

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For example for the matrice ones the set (Mn*p(R),+,.) is already a vectorial space for all (n,p) in N ^2

worldly relic Oct 20, 2023, 4:19 AM

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zenith crescent You could also prove that these are subspaces

My professor told me I need to prove all ten axioms haha

zenith crescent Oct 20, 2023, 4:22 AM

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worldly relic My professor told me I need to prove all ten axioms haha

Oh okay

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Well then for scalar multiplication take two scalars a and b and two matrices A and B and prove that (a+b).A=a.A+b.A that (a*b).A=a.(b.A) a.(A+B)=a.A+a.B etc…

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Same thing with polynomials

worldly relic Oct 20, 2023, 4:50 PM

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Thank you 😊 @zenith crescent

#Vector spaces