# space

1. ### Time Sample Space and Event

A telephone call from a certain person is received some time between 7:00 A.M. and 9:10 A.M. every day. Define a sample space for this phenomenon, and describe the event that the call arrives within 15 minutes of the hour. The sample space is straight forward S = {[7, 55/6]}, but the event is...
2. ### Drawing Two Coins

Define a sample space for the experiment of drawing two coins from a purse that contains two quarters, three nickels, one dime, and four pennies. Q - Quarter N - Nickel D - Dime P - Penny S = {QQ, QN, QP, QD, DN, DP, NP, NN, PP} This is the book answer. I am wondering why the sample space did...
3. ### xyz-space

Sketch a graph in the xyz-space and identify the plane as parallel to the xy-plane, xz-pane, or yz-plane and sketch a graph. a) y = 4 b) x = -2 ------------------ I don't understand why the answer for (a) is plane parallel to xz-plane!
4. ### Sample Space of a Coin

(a) What is the sample space of tossing three coins? (b) A coin is tossed 3 times in a succession, and the total number of times heads comes up is noted. What is the sample space? Is the answer for those 2 questions the same?
5. ### Linear Algebra: help with inner product space

I don't understand how to solve this type of problems and I can't find solved examples anywhere in my textbook or the internet. Can you help me out? In R^3 it's given the symmetric, bilinear form F: R^{3}\times R^{3}\rightarrow R : F((x_{1},y_{1},z_{1}),(x_{2},y_{2},z_{2})) = 3...
6. ### How to you put a space in your formulas on this website?

I have tried various methods seen on this forum, across the net and at physics forum and none of them are working for me. I have tried the following within tags: \ \, \quad \qquad ~...
7. ### Is my vector space proof valid?

Question: The sum S + T contains all sums s + t of a vector s in S and a vector t in T. Show that S + T satisfies all the requirements (addition and scalar multiplication) for a vector space). My proof: let s = \mu s_{1} +\lambda s_{2} let t = \mu t_{1} +\lambda t_{2} where lambda and mu...
8. ### Proof of inner product relation in a Hilbert space

Hello everyone I have been given a task where I need to prove, \forall \textbf{v} \in H, the following formula: <\textbf{v},\sum \limits^{\infty}_{k=1}c_k \textbf{v}_k>=\sum \limits^{\infty}_{k=1}\bar{c_k}<\textbf{v}_k, \textbf{v} > Where < \: \cdot \: , \: \cdot \: > is an inner product...
9. ### Find a counterexample on a normed vector space

Hello, I'm wonder if it is possible to find a sequence of functions (f_n) defined on a normed vector space (E,\|\cdot\|) to precise, such that (f_n) converge pointwise to a function f\in E \|f_n-f\| does not tend to zero \exists g\in E, which is not "equal almost everywhere to f", and such...
10. ### Help calculating a point in 2d space on a rotating right angle triangle

I am trying to solve for a point on a triangle that rotates around a fixed point. For ease of calculation this point is at X: 0 Y: 0 The length and width of the triangle are always fixed, the only thing that changes is the rotation angle. How can I solve for X: ??? and Y: ??? taking into...
11. ### Hausdorff space

Let $X$ be a topological space, and let $A$ be a subspace of $X$ with $\overline{A}=X$. Show that if $f,g:X\to Y$ are continuous functions, where $Y$ is a Hausdorff space, and $f(a)=g(a)$ for all $a\in A$, then $f=g$. ---- What we know: 1) Since $f,g$ are continuous, then the subset...
12. ### Topological space and continuous function

Let $X$ be a toological space. Suppose that $f$ and $g$ are continuous maps $X\to \mathbb{R}$. Define the function $(f+g)(x)$ by $(f+g)(x)=f(x) + g(x)$. Show that $$(f+g)^{-1}((a,b))=\bigcup_{s,t\in \mathbb{R}}f^{-1}((s,t))\cap g^{-1}((a-s,b-t))$$ and deduce that $f+g$ is continuous. Here's...
13. ### Cauchy sequence in an Hilbert space

Let H be an hilbert space Assume {e_n} is an orthonormal set. Prove that there cannot exist an element f in H such that e_n --> f (Meaning that ||e_n-f||-->0 as n approaches infinity) What I have tried: Since Hilbert is a complete inner product space, every cauchy sequence converges to a...
14. ### complement and null space

if A is a submodule of M, M = R^n, the null space of Q is defined as {x|Qx = 0} where Q is n by n matrix with entries in M. The complement of A is B so M = A+B( inner direct sum). I am trying to prove that if A has a complement in M, so A is the null space of Q for some Q( n by n matrix with...
15. ### Converting spherical coordinates to cartesian in rotated space

Hello, I am working on a program that draws lines by converting spherical coordinates into cartesian coordinates. I use the following equations to calculate the cartesian coordinates of a point based on its distance, azimuthal angle, and polar angle from another point. The y axis is...
16. ### Motion in Space

r(t) is the position of a particle in space at time t. Find the particle's velocity vector. Next find the particle's speed and direction of motion at time t. Finally, write the particle's velocity at the time t as a product of it's speed and direction. r(t) = (t + 1)i + (t^{2} -1 )j + 2tk t...
17. ### finding the base of a vector space

Hi guys I have been doing a few questions regarding vector spaces Given S={(1,-1,1,0), (1,0,1,1) (0,1,1,0)} T= {(x,y,z , 2x+y-z): x,y,z \in R} I am trying to show that S is a basis of T, I have shown that is linearly independent to show that S spans T i have done the following: \alpha...
18. ### I need help rewriting a linear three space equation in slope intercept form

I want to know how to write a linear three space equation in slope intercept form so three space graphers like geogebra will recognize and display correctly. I have a question asking to describe the shape of the intersection of the plane z=-3 and the plane y=z in three space. So I wrote this...
19. ### inner product space question

need to prove that the following (in the image) is inner product space. I just got stuck in proving the positive-definiteness. If for example I take p that isn't 0, why does the integral has to be positive? what if I take t to be the root of p? don't I get 0?
20. ### Is A Subspace of a 3D Vector Space a 2D Plane?

Not sure how to elaborate on the question more than the title, so I'll just reiterate: Is A Subspace of a 3D Vector Space a 2D Plane? I'm just trying to visualize/understand this concept.