it is a big mess for me understanding vector spaces subject inlinear algabra, i

Question

it is a big mess for me understanding vector spaces subject inlinear algabra, i need to answer the following Q? where these aresubspases or not Of R3? i have the answers but i need to undestandwhy? means justify? 1) plane of( b1,b2,b3)vectors with b1 2)plane of vectors b with b1=1 3) all combinations of two given vectors (1,1,0) and(2,0,1) 4) the plane of vectors (b1,b2,b3) that satisfyb3-b2+3b1=0 thanks very much it is a big mess for me understanding vector spaces subject inlinear algabra, i need to answer the following Q? where these aresubspases or not Of R3? i have the answers but i need to undestandwhy? means justify? 1) plane of( b1,b2,b3)vectors with b1 2)plane of vectors b with b1=1 3) all combinations of two given vectors (1,1,0) and(2,0,1) 4) the plane of vectors (b1,b2,b3) that satisfyb3-b2+3b1=0 thanks very much

Explanation / Answer

First off, let me say that you should post linearalgebra questions in the higher math section of Cramster, not inthe algebra section. You will have better success gettinganswers there. Second, I don't have Strang's book, but surely something ismissing in your copy of the questions 1 and 2. Now, for the moment you've been waiting for (at least, part ofthe moment you've been waiting for). 3) to be a subspace, it would have to also be a space, onethat is included in the larger space. That means it must be "closed" under addition andmultiplication, and include the zero vector, I believe. All combinations or the two vectors given would also be closedunder addition, but I don't think you can make the zero vector fromthem, so I think the answer is No, not a subspace. 4) We can see from the definition of the plane that 0 isincluded. also, it seems to me that any vector on thatplane described by b3 - b2 +3B1 = 0 could be addedto any other and still remain within that definition. That is, the sum of the two vectors would still be on that sameplane. Honestly, I am not 100% sure, but that's my thought,so my thought is Yes, subspace of R3. If you repeat this question on the higher math section, andmake sure parts 1 and 2 are exactly copied, someone better atlinear than I am will answer you.

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