Subspace Definition and 560 Threads

I just wanted to know if my answer is acceptable. Q: S={(x,y,z) E \mathbb{R}^{3} l x^2 + y^2 +z ^2 =0} Is it a subspace of \mathbb{R}^{3}? My answer: It is a subspace if x=0, y =0, z= 0 Let u=(0,0,0) u2=(0,0,0) and k be a scalar u + u2 = (0,0,0) Closed under addition...

TNG season 6 Relics Well I figure that they likely don't exist. But the theory that you could construct the sphere entirely around a star. Is this even plausible? Wouldn't heat and radiation eventually build up quite a bit.

I have heard the term 'subspace' repeated many a time in various science fiction TV shows, Star Trek and Stargate the most notable. What is this subspace they refer to, does it really exist. Thankyou.

Hi. I need to find a base for the subspace V in R3 which has the equation x+2y+3z=0 Can someone please tell my if the space I'm looking for is [1 0 0;0 2 0;0 0 3] ? If not, please explain what I'm doing wrong

Hi everyone, I was hoping someone could help me with something. Could someone explain to me exactly what this expression means: H = {(a+b) + (a - 2b)t + bt^2 | a E R, b E R} the purpose is to find the dimension of the given subspace, which I know how to do, I have just never seen this...

Hi everyone, I was hoping someone could help me with something. Could someone explain to me exactly what this expression means: H = {(a+b) + (a - 2b)t + bt^2 | a E R, b E R} the purpose is to find the dimension of the given subspace, which I know how to do, I have just...

Let V be the subspace of F([0,1],R) generated by the functions f1, f2, f3 given by: f1(x)=1/(x+1) , f2 (x) = 2-x and f3(x) = x^2 for all x element of [0,1]. Find a basis of the subspace U of V that consists of all the functions g of V such that g(0) = g(1)...

Hi guys. I need some help with question #5 from my assignment. If someone can just tell me how to get the question started, it would be great. Thanks :smile: http://img34.exs.cx/img34/8320/algebra1.jpg

Hi guys. I need some help with question #5 from my assignment. If someone can just tell me how to get the question started, it would be great. Thanks :smile: http://img34.exs.cx/img34/8320/algebra1.jpg

I have been trying this problem for hours. I can't believe I can't get it. The question is "Find a subset U of R^2 such that U is closed under scalar multiplication but is not a subspace of R^2". I know that for U to be a subspace 0 must be an element of U and U has to be closed under scalar...