Hi there, I literally got stuck on this question, it would be
great if someone can give me help, many thanks in advance!
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Hi there, I literally got stuck on this question, it would be great if someone can give me help, ...
Hi. I'm having trouble with this question in my Topology class. Can I get some help on this?? Tha...
Hi. I'm having trouble with this question in my Topology
class.
Can I get some help on this?? Thank you.
(3) Define a function d: R 2 x R2 → R by d(x, y) = max(ki-yil. 12.2-U21) for any two points x-(xi,T2), y-(yi,y2) є R2. Then d is a metric for R2. Prove that {(r,y) є R2lr+y > 0} is an open subset of the metric space (R2, d) and that {(x, y) є R2 1 x + y >...
row reduction in uncountable dimension. Part 2. (Row-reduction in countably-infinite dimension) Let V denote the vector...
row reduction in uncountable dimension.
Part 2. (Row-reduction in countably-infinite dimension) Let V denote the vector space of polynomials (of all degrees). Recall that V is an infinite-dimensional vector space, but it has a countable basis. Consider Te Hom(V, V) defined as T(p())5p () 10p(x - 1) 2.1. Write T as an oo x oo matrix, in the standard basis 1,X, x2, 13,... of V 2.2. Write T as an oo x oo matrix, in the basis 1, + 1,...
Question 2: For this question, consider the non-standard pairing on the space of real polynomials P...
Question 2: For this question, consider the non-standard pairing on the space of real polynomials P given by g) = Lif(t)g(x).rº dr. (a) Prove that (,) defines an inner product on P. (b) Let O be the set of odd polynomials, i.e. f(r) € P such that f(x)= -f(-r). Show that is a subspace of P. (c) Explain why g() = 5x2 - 3 is in 0+ (the orthogonal complement of O with respect to (>). (d) Let P<2 denote...
The question that is being asked is Question 3 that has a red rectangle around it....
The question that is being asked is Question 3 that has a red
rectangle around it.
The subsection on Question 7 is just for the Hint to part d of
Question 3.
Question 3. Lul (X', d) be a metric space. A subsct ACX is said to be Gy if there exista a collection of open U u ch that A- , , Similarly, a subact BCis said to be F if there exista collection of closed sets {F}x=1 such...
New problems for 2020 1. A topological space is called a T3.space if it is a...
New problems for 2020 1. A topological space is called a T3.space if it is a T, space and for every pair («,F), where € X and F(carefull), there is a continuous function 9 :X (0,1 such that f(x) 0 and f =1 on F. Prove that such a space has the Hausdorff Separation Property. (Hint: One point subsets are closed.] 2. Let X be topological space, and assume that both V and W are subbases for the topology. Show...
Hi there, is this possible to give me a help on this probability question, literally in a desperate situation! Thanks a lot! Problem 4 (20p). Let α > 0, and for each n N let Xn : Ω R be a random v...
Hi there, is this possible to give me a help on this probability
question, literally in a desperate situation! Thanks a lot!
Problem 4 (20p). Let α > 0, and for each n N let Xn : Ω R be a random variable on a probability space (Ω,F,P) with the garnma distribution Γαη. Does there exist a random variable X:S2 → R such that Xn → X as n → oo?
Problem 4 (20p). Let α > 0, and for...
I got stuck on this question about Expected Value, would be great if someone can give...
I got stuck on this question about Expected Value, would be great if someone can give me a hand. Thanks in advance! Question: Determine all the values a, b such that E((Y - a - bX)^2) is minima. X and Y are real valued random variables.
Linear algebra, I need someone to tell me how to get T(1)=1,1,1 T(x)=-1,0,1 T(x^2)=1,0,1 T(x^3)=-1,0, 1...
Linear algebra, I need someone to tell me how to get
T(1)=1,1,1 T(x)=-1,0,1 T(x^2)=1,0,1 T(x^3)=-1,0, 1 I don't
have any clue to find this. please follwo the comment
WHAT FORMULA SHOULD I PLUG IN WHEN I PLUG IN T(1),
T(X)......
How about this: Problem 2. Let P3 = Span {1,2,22,23 , the vector space of polynomials with degree at most 3, and let T : P3 → R3 be the linear transformation given by T(p)p(0) 1000 1) Find the matrix...
can anybody explain how to do #9 by using the theorem 2.7? i know the vectors...
can anybody explain how to do #9 by using the theorem
2.7?
i know the vectors in those matrices are linearly independent,
span, and are bases, but i do not know how to show them with the
theorem 2.7
a matrix ever, the the col- ons of B. e rela- In Exercises 6-9, use Theorem 2.7 to determine which of the following sets of vectors are linearly independent, which span, and which are bases. 6. In R2t], bi = 1+t...
Help A3: This question illustrates how different bases for spaces of polynomials can help solv- ing...
Help
A3: This question illustrates how different bases for spaces of polynomials can help solv- ing mathematical problems. In particular, we look at the use of Lagrange polynomials for polynomial interpolation. Let be the space of polynomials of degree at most two. (a) We define the mapping T: P2R3 by evaluating a given polynomial f i.e P2 at 12,, T(f) = f(2) f(3) Show that this is a linear transformation. (b) Consider the bases B b, b2, bs1,t, and G9929s),...
Hi. I'm having trouble with this question in my Topology
class.
Can I get some help on this?? Thank you.
(3) Define a function d: R 2 x R2 → R by d(x, y) = max(ki-yil. 12.2-U21) for any two points x-(xi,T2), y-(yi,y2) є R2. Then d is a metric for R2. Prove that {(r,y) є R2lr+y > 0} is an open subset of the metric space (R2, d) and that {(x, y) є R2 1 x + y >...
row reduction in uncountable dimension.
Part 2. (Row-reduction in countably-infinite dimension) Let V denote the vector space of polynomials (of all degrees). Recall that V is an infinite-dimensional vector space, but it has a countable basis. Consider Te Hom(V, V) defined as T(p())5p () 10p(x - 1) 2.1. Write T as an oo x oo matrix, in the standard basis 1,X, x2, 13,... of V 2.2. Write T as an oo x oo matrix, in the basis 1, + 1,...
Question 2: For this question, consider the non-standard pairing on the space of real polynomials P given by g) = Lif(t)g(x).rº dr. (a) Prove that (,) defines an inner product on P. (b) Let O be the set of odd polynomials, i.e. f(r) € P such that f(x)= -f(-r). Show that is a subspace of P. (c) Explain why g() = 5x2 - 3 is in 0+ (the orthogonal complement of O with respect to (>). (d) Let P<2 denote...
The question that is being asked is Question 3 that has a red
rectangle around it.
The subsection on Question 7 is just for the Hint to part d of
Question 3.
Question 3. Lul (X', d) be a metric space. A subsct ACX is said to be Gy if there exista a collection of open U u ch that A- , , Similarly, a subact BCis said to be F if there exista collection of closed sets {F}x=1 such...
New problems for 2020 1. A topological space is called a T3.space if it is a T, space and for every pair («,F), where € X and F(carefull), there is a continuous function 9 :X (0,1 such that f(x) 0 and f =1 on F. Prove that such a space has the Hausdorff Separation Property. (Hint: One point subsets are closed.] 2. Let X be topological space, and assume that both V and W are subbases for the topology. Show...
Hi there, is this possible to give me a help on this probability
question, literally in a desperate situation! Thanks a lot!
Problem 4 (20p). Let α > 0, and for each n N let Xn : Ω R be a random variable on a probability space (Ω,F,P) with the garnma distribution Γαη. Does there exist a random variable X:S2 → R such that Xn → X as n → oo?
Problem 4 (20p). Let α > 0, and for...
Linear algebra, I need someone to tell me how to get
T(1)=1,1,1 T(x)=-1,0,1 T(x^2)=1,0,1 T(x^3)=-1,0, 1 I don't
have any clue to find this. please follwo the comment
WHAT FORMULA SHOULD I PLUG IN WHEN I PLUG IN T(1),
T(X)......
How about this: Problem 2. Let P3 = Span {1,2,22,23 , the vector space of polynomials with degree at most 3, and let T : P3 → R3 be the linear transformation given by T(p)p(0) 1000 1) Find the matrix...
can anybody explain how to do #9 by using the theorem
2.7?
i know the vectors in those matrices are linearly independent,
span, and are bases, but i do not know how to show them with the
theorem 2.7
a matrix ever, the the col- ons of B. e rela- In Exercises 6-9, use Theorem 2.7 to determine which of the following sets of vectors are linearly independent, which span, and which are bases. 6. In R2t], bi = 1+t...
Help
A3: This question illustrates how different bases for spaces of polynomials can help solv- ing mathematical problems. In particular, we look at the use of Lagrange polynomials for polynomial interpolation. Let be the space of polynomials of degree at most two. (a) We define the mapping T: P2R3 by evaluating a given polynomial f i.e P2 at 12,, T(f) = f(2) f(3) Show that this is a linear transformation. (b) Consider the bases B b, b2, bs1,t, and G9929s),...
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