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Vector spaces

FilipVz

New member
Oct 21, 2013
8
Hi,

can somebody help me with the following problem:


Exercise 4.png

Thank you. :)
 

Sudharaka

Well-known member
MHB Math Helper
Feb 5, 2012
1,621

Deveno

Well-known member
MHB Math Scholar
Feb 15, 2012
1,967
Lazy, hazy proof:

An isomorphism is, among other things, a bijection. So all one needs to do is show 2 things:

1) A linear injection preserves linear independence
2) A linear surjection preserves spanning

These two facts together show that the image under our given isomorphism of a basis for the first vector space is a basis for the second space, and since the isomorphism is bijective, they have the same cardinality.