Re: Linear Algebra


jennifer wrote:

Please do not top-post.




Arturo Magidin wrote:
In article <1157235524.037307.90520@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
jennifer <scrilla_12_1999@xxxxxxxxx> wrote:
Ok, is {(x_1,x_2,x_3) in F^3:x_1*x_2*x_3 = 0} a subspace of F^3.

I noticed that it is as, if I let x_1 = x_2 =x_3 = 0, then x_1*x_2*x_3
= 0 and thus, (0,0,0) is in the subspace and i am sure the other
properties follow suit.

Good for you. Too bad it's wrong.


Am I right in assuming this?

No.

Can you think of a situation in which two vectors would satisfy the
condition, but their sum would not?


It is not a subspace as it is not closed under addition.

I don't know about your professor. But if one of my students answered
this problem
by simply saying "it is not closed under addition", that student would
receive very
little, if any, credit.

PROVE that it is not closed under addition. Exhibit two ->explicit<-
vectors
which are in the set, but whose sum is not. Show the two vectors are
in the set, and show their sum is not.

Arturo Magidin

.

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