In mathematics, and more specifically in linear algebra, a linear subspace, also known as a vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when the context serves to distinguish it from other types of subspaces.
Let U be a subspace of Rn
If aX is in U, where a is non zero number and X is in Rn, show that X is in U
THis seems so obvious... but i m not sure how to show this by a proof
aX is in U and aX is in Rn for sure and U is a subspace of Rn.
Is it true that if U is closed under scalar...
I'm studying for my exam on monday and i saw ap roblme that says:
Determine if the following is a subspace of R^3.
For it to be a subspace it has to pass
1) must have the zero vector
2) closure under addition
3) closure under multiplaication
here is my work...
I want to project a vector from R3 onto a subspace.
I'll let the bases for the subspace be [a,b,c]T
(my T's mean transpose)
---
I have the defintion for vector projection
p = (<u,v>/<v,v>)*v
---
I know v will be the [a,b,c]T vector but what is u?
The only thing I could think of is let it...
The functions e^x and e^2x
I have to find the dimension of the vector subspace spanned by this set.
Im not sure where to start, I do know how to solve other problems asking the same question just different function. Any help would be greatly appreciated.
thanks
a.p
The functions e^x and e^2x
I have to find the dimmensions of the vector subspace spanning the set.
I understand how to solve other problems like involving matrices and row reducing, but this function i don't know where to start and how to figure out the dimensions. Any help would be greatly...
I'm having a hard time understanding some things about vector subspaces.
I have two problems that I am supposed to determine if the sets are subspaces of R^2.
I know both sets are not subspaces but I don't really understand why or how to prove it for that matter. Can anyone shed some...
Suppose U, V are proper subsets of Rn and are subspaces and U is a proper subset of V. PRove that V perp is a proper subset of U perp
Ok SO let U ={u1, u2, ..., un}
let V = {v1,...vn}
let V perp = {x1,x2,..., xn}
let U perp = {w1,...wn}
certainly u1 . w1 = 0
(u1 + u2 ) . (w1+w2) = 0
cu1...
Hi everone,
quick question: if i have 3 vectors and I need to know basis of the subspace they span, so I write each vector as rows of a matrix and when I reduce it, is it the basis of rowspace or column space of matrix that is the basis of the subspace that vectors span?
Thanks in advance.
I'm stumped by this problem:
let W be the subspace of C[0,1] spanned by S={sin^2(x),cos^2(x),cos2x}
a) explain why S is not a basis for W
it's because S not linearly independent
b) find a basis for W
please help me with this one...
TIA.
Hi,
I'm just learning for my linear algebra exam and I wonder if somebody could give me an example of a nontrivial subspace which has as many dimensions as the original space.
Thanks a lot
Hi,
I'm just learning for my linear algebra exam and I wonder if somebody could give me an example of a nontrivial subspace which has as many dimensions as the original space.
Thanks a lot
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...