Linear Algebra-Subspace Functions

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The discussion revolves around verifying that the set W, defined as functions f in F(ℝ) satisfying f(-x) = f(x), is a subspace of F(ℝ). Participants confirm that the zero function is in W and discuss closure under addition, demonstrating that (f+g)(x) = (f+g)(-x). The main confusion arises around verifying closure under scalar multiplication, with clarification needed on the definitions of vector spaces and zero vectors. Emphasis is placed on understanding the definitions and properties of functions within the context of vector spaces. The conversation highlights the importance of grasping foundational concepts in linear algebra to solve such problems effectively.
  • #61
You probably just need to pay more attention to the definitions, be more careful with your statements, and do more exercises. Getting a copy of the textbook would probably be a good start. :smile:
 
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  • #62
I have always been lazy to the "statements", never thought they were really important, unless it is the conclusion other than that the answer is pretty obvious. In calculus questions for integrals and derivative questions like rate of change and etc. I never put Let x be that so I almost always lost marks on that. Because with all the assigning variables sometimes confuses me on what they mean and confused them with the important variables. I am still thinking in a concrete way so I just go by formula. I really need to get used to this because I am taking a course that has a lot of Proofing next. and my english isn't as good either :P
 

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