Linear Algebra Example Problems - Subspace Example #4

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We work with a subset of vectors from the vector space R2. We show that this subset of vectors is NOT a subspace of the vector space.

This problem is similar to Subspace Example #3, but the subset of R2 used in the problem is slightly different so the subspace criteria that pass/fail are slightly different as well.

Recall, in order for a subset of a vector space to be a subspace, it must satisfy three criteria:
1) Contains the zero vector, 2) Is closed under addition, and 3) Is closed under scalar multiplication.

If any of these fail, the subset is not a subspace. In this problem, both 1) and 2) are true, but since 3) fails the subset of R2 is not a subspace of R2.

  1. Adam Panagos
  2. linear algebra subspace
  3. vector space examples
  4. Vector Space
  5. Math
  6. linear subspace examples
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Комментарии
Автор

THIS video definitely save my linear course. WHY these professors in college dont just display your video on the class. i promiss the average grade will get into new level.VERY GOOD VIDEO!! PLEASE KEEP GOING

michaeldai
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You deserve way more views. Very good videos and explanations of maths. Thanks

patrickmoloney
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Awesome explanation. This isn't as hard as I thought it'd be. Thanks!

SkyRanger
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yes that makes perfect sense, just got it. thanks for that clarification. y cant be less than 0 as it is defined as greater than equals to zero from the start. thanks for the list of 6 exercises revising for my test tomorrow. its been great

picsou
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great explanation
thanks and keep up the good work

kalanadesilva
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do u have a Pateron or anything? My next exam is do-or-die for me and u have me feeling pretty confident!!! Thanks man

Kuminbreakuoff
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You cant put >= oo . Can you put in a parameters the value of infinity?

siderminerkgl
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what if y1 is -5 and y2 is -1. which gives us a y3 of -6 which implies y3 is <0. does that not make Y out of the range and hence not closed under addition?

picsou
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sir liner algebra writter fridberg 1.6 exercise 14 nu. question .please explain

harsitagupta
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sir when x is less than or equal to 0, then how the sketch of the graph consists 1st quadrant also?

shayantnandi
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You can't choose 2, 1 because x<= 0 still it's not subspace so doesn't matter.... Plz take care of that...

yashraj