Bases Definition and 281 Threads

Prove that $.0222\ldots$ (base 3) $= .1$ (base 3) $= \frac{1}{3}$ (base 10).First, we will show $.0222\ldots$ (base 3) $= \frac{1}{3}$ (base 10). \begin{alignat*}{3} 2\left(\frac{1}{3^2} + \frac{1}{3^3} + \frac{1}{3^4} + \cdots\right) & = & 2\sum_{n = 2}^{\infty}\left(\frac{1}{3}\right)^n\\ & =...

I am doing a lab this week where the objective is to use acids and bases and a microscale extraction to separate three solids in a mixture. The mixture in question is a mixture of naphthalene, benzoic acid, and ethyl 4-aminobenzoate. It will then be put through a series of solvents and...

Homework Statement I have 2 bases, a = {1, x, x^2} and b = {-2 - 2x + 3x^2 , 1 + 2x - x^2 , -1 - x + 2x^2} of P2. Find the transition matrix Pab. How is this done?? Homework Equations Since this is Linear Algebra, there aren't really any relevant "Equations" as such. More logic...

Homework Statement I have 2 bases, a = {1, x, x^2} and b = {-2 - 2x + 3x^2 , 1 + 2x - x^2 , -1 - x + 2x^2} of P2. Find the transition matrix Pab. How is this done??Homework Equations Since this is Linear Algebra, there aren't really any relevant "Equations" as such. More logic based...

I'm a little confused about certain assumptions usually made in GR as to how rigorous they are mathematically speaking. For instance the assumption generally presented without proof that GR spacetime manifold is a Hausdorff space seems not to be warranted given the fact that pseudometric spaces...

Homework Statement Given that b>1,b\in\mathbb{Z},c_{0},c_{1},...,c_{m}\in\{0,...,b-1\}, 0\leq c_{m+1}\leq b-1, and c_{m+1}b^{m+1}=(\sum\limits _{k=0}^{m+1}c_{k}b^{k})\text{mod }b^{m+2}-c_{0}-c_{1}b-c_{2}b^{2}-...-c_{m}b^{m}, show that c_{m+1}\in\mathbb{Z}. Also, \sum\limits...

Say we have the same state \boldsymbol{\psi_r} in momentum basis, or \boldsymbol{\phi_p} in position basis. I want to make either a position observation or a momentum observation. How do I write the operation and the result mathematically, \mathbf{r} \boldsymbol{\psi}, \mathbf{r}...

I'm thinking of expanding the numerical value of a real number in different bases. I want you guys to ensure some things for me so I know I'm not wrong. If X is the representation of a in the base B and Y is the representation of b in the same base(radix), can we say that X+Y = a+b? In...

Hi: I have a problem about combine bases from subspaces. This is part of orthogonality. The examples as following: For A=##\begin{bmatrix} 1 & 2 \\ 3 & 6 \end{bmatrix}## split x= ##\begin{bmatrix} 4 \\ 3 \end{bmatrix}## into ##x_r##+##x_n##=##\begin{bmatrix} 2 \\ 4...

Bases of a Linear transformation (Kernel, Image and Union ? http://dl.dropbox.com/u/33103477/1linear%20tran.png For the kernel/null space \begin{bmatrix} 3 & 1 & 2 & -1\\ 2 & 4 & 1 & -1 \end{bmatrix} = [0]_v Row reducing I get \begin{bmatrix} 1 & 0 & \frac{7}{9} & \frac{-2}{9}\\ 0 & 1...

Homework Statement Find the bases for the eigen spaces? I handwrote the question and my work so it would be easier to read and attached it so see attachment. Homework Equations The Attempt at a Solution My work is on the attachment. My question is this what do I do when I have 3...

There is a lot of crazy conspiracy chatter, if its true, then what type of equipment do I need to see the moon bases or Mars bases? Thank you. I'm a real human, curious son of a b.

http://dl.dropbox.com/u/33103477/Union.png Omiting zeroes because they add nothing: \begin{bmatrix} 3 & 1 & 7 & 4\\ 5 & 6 & 7 & 3 \end{bmatrix} RREF \begin{bmatrix} 1 & 0 & \frac{35}{13} & \frac{21}{13}\\ 0 & 1 & \frac{-14}{13}& \frac{-11}{13} \end{bmatrix} Hence the basis is...

I need some help or at least some assurance that my thinking on linear transformations and their matrix representations is correct. I assume when we specify a linear transformation eg F(x,y, z) = (3x +y, y+z, 2x-3z) for example, that this is specified by its action on the variables and is not...

Homework Statement Data for Question B: (initial)[CH3COOH] = 0.500 mol dm–3 and) eqm [CH3COOH] = 0.200 mol dm–3; (initial)[CH3COO–] = 0.300 mol dm–3 and) eqm [CH3COO–] = 0.300 mol dm–3; The Attempt at a Solution Question A) " FInd the pH of a mixture of 50.0 cm3 of 0.100 mol...

I've been given a question on how to tell whether a compound is an acid or base or neautral in an aquesous solution. Na2CO3 Please help.

According to the Wikipedia article a composite number n is a strong pseudoprime to at most one quarter of all bases below n . Do Fermat pseudoprimes have some similar property ? Is it known what is the largest number of bases for which composite n , that is not Carmichael number is...

hello this question from my coarse notes has been giving me some trouble so i thought i would ask for some help on here, http://img88.imageshack.us/img88/9764/asfar.jpg i understand that since the bases are bases of the same solutions then they are just a multiple of each other, but...

Here is my solution, I think I have part i) done OK, but I'm not sure about how to proceed with part ii). I suppose I need to show that both determinants of the base change matrices Cij and Dij are = ±1?Thanks

I was told that when a base is dissolved in water, the ions form ion pairs so it is difficult to separate them completely; is this true? And if so, why wouldn't this apply to acids?

I am currently trying to go between any two bases which are between and including base 2 to base 10. (i.e, base 10 to base 3, base 4 to base 6, etc...). Is there an equation or set of formulas for a one-step transition between the bases (or one-way method, rather than converting to base-10 then...

Homework Statement http://img856.imageshack.us/img856/5586/screenshot20120121at328.png The Attempt at a Solution I propose the vectors x,x^2,x^3 form a basis of V. To test for linear independence, let 0 = a_1 x + a_2 x^2 + a_3 x^3, where a \in R. A polynomial is 0 iff all of its...

When reading in Griffiths and on Wikipedia about the vector space formulation of wavefunctions, i am constantly faced with the statement that a vector can be expressed in different bases, but that it's still the same vector. However, I'm having a hard time imagining what it is about a vector...

Hello everyone, I am currently learning about bases, and I am confused about different types of bases. I understand how to obtain a basis for the null space of A or a basis for the range of A. I recently ran into a problem that simply asked me to find a basis for A. What does this mean? Does...

1. Homework Statement See Attachment. Help with b) c) will be appreciated. 3. The Attempt at a Solution For the third question, my approach is sub in values for a and b which correspond to the co-effs. of the given basis. Then assemble a matrix from them. Eg...

Finite-dimensional V and W are linearly isomorphic vector spaces over a field. Prove that if \{v_{1},...,v_{n}\} is a basis for V, \{T(v_{1}),...,T(v_{n})\} is a basis for W. My attempt at a proof: Let T:V\rightarrow W be an isomorphism and \{v_{1},...,v_{n}\} be a basis for V. Since T is an...

Homework Statement See Attachment. The Attempt at a Solution For the first two questions, I know I have to sub in values for a and b. But, I'm not sure what the output matrix is. The 3rd q, to prove B is Basis for R^3. I just have to row reduce [(1,5);(1,6)] to get [(1,0);(0,1)] right...

Homework Statement Show that the set W consisting of all vectors in R4 that are orthogonal to both X and Y is a subspace of R4. Here X and Y are vectors such that X = (1001) and Y = (1010). Part b) Find a basis for W. The Attempt at a Solution So I know to satisfy being a...

Say I have (a+b+c)^n and I want to split it apart into a^something + b^something + c^something. Is this easily done?

I am going through Sn1, E1, Sn2, E2 reactions and I'm trying to figure out if the reaction involves a nucleophile (strong/weak) or a base (strong/weak). I understand that you can differentiate nucleophiles and bases by their pKa value but that doesn't quite help me out, since I'm not given...

Homework Statement Which of the following sets S are bases for the vector space V=\mathbb{R}^3? (a) S=\left\{ \begin{bmatrix} 1 \\ 1 \\ 0 \end{bmatrix} , \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} , \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} \right\} (b) S=\left\{ \begin{bmatrix} 1 \\ 1...

I am reading the book Introduction to Quantum Mechanics by David Griffiths and have come to the section on Dirac notation. It explains that the state of a quantum system is represented by a vector |β(t)> living out in Hilbert space, and, as with any vector, is independent of the choice of basis...

This guy is stealing my bases! nvm delete this please i got it

Homework Statement Let T be the linear transformation T=[1, 3, 2, 6] (the matrix has 1 and 3 on the top row and 2 and 6 on the bottom row) relative to the standard basis Find the matrix relative to the basis B= {(1, 2), (-3, 1)} Homework Equations The Attempt at a Solution So what I did was...

I'm unsure as to if I am using the correct terminology, but what I mean by this is log = logarithm in base 10. ln = logarithm in base e. logx = logarithm in base x. Upon some investigation, I found that log(a)/ln(a)=log(b)/ln(b) where a and b are constants, meaning that there is a ratio...

Homework Statement [PLAIN]http://img193.imageshack.us/img193/3662/unledmcg.png The Attempt at a Solution I rewrote the whole thing in dictionary x_3 = 15 - 8x_1 - 4x_2 x_4 = 7 - 2x_1 - 6x_2 z = 0 + 22x_1 - 12x_2 x_i \geq 0 1\leq i \leq 4 a) So my basis/bases is x...

I tried googling this topic and basically all I could find was sites saying they neutralise each other - I know that. But why is it that when you mix say a drop of pH 14 solution with a lot of pH 1 solution that they react rather violently and the acid sprays everywhere? If someone could maybe...

Homework Statement Let T: R3 - R3 be the linear operator given by T = -y + z -x + z x + y Find a basis B' for R3 relative to which the matrix for T is diagonal using the standard basis B for R3. Homework Equations [T]B' = P-1[T]BP The Attempt at a Solution...

Homework Statement I'm having problems understanding amphoteric acids and bases. I know amphoteric means that it can act as an acid or base, but when the question asks me to write the equation to support this statement, I always get it wrong :confused: Homework Equations HSO4^-1 is an...

I used to think I was master of any high school math course until I came across this log equation in a calculus textbook. \log_{2}x + \log_{5}(2x+1) = \ln x I use the change of base to convert everything to one base and then I get down to: (2x+1)^{\ln2} = x^{\ln2\ln5 - \ln5} I have no...

My book says the following: NH4NO3 is weakly acidic as a salt because it is composed of the conjugates of the base NH3 and the strong acid HNO3. Why does that make it weakly acidic exactly?? Is it because the HNO3 is a strong acid, therefore it won't steal the protons that are...

My background in linear algebra is pretty basic: high school math and a first year course about matrix math. Now I'm reading a book about finite-dimensional vector spaces and there are a few concepts that are just absolutely bewildering to me: dual spaces, dual bases, reflexivity and...

I'm trying to follow a proof in this video, #20 in the ThoughtSpaceZero topology series. I get the first part, but have a problem with second part, which begins at 8:16. Let there by a topological space (X,T). Let x denote an arbitrary element of X. Definition 1. Topological base. A set B...

Homework Statement Let A be an m x n matrix such that the homogeneous system Ax=0 has only the trivial solution. a. Does it follow that every system Ax=b is consistent? b. Does it follow that every consistent system Ax=b has a unique solution? The Attempt at a Solution So if the homogeneous...

I have recently read some articles that deal with future technologies such as invisibility and teleportation. There are some magazines, websites and scientists such as Micho Kaku who make future predictions based on the latest cutting-edge technologies and scientific data. My question is...

Sorry guys, I can't seem to grasp the concept: It deals with acids and bases. When the acid donates the proton, to the base, how do we know how many is transferred and how many the base can accept? This is where I am stumped. Homework Statement What ions are formed when nitric...

I have a question about Garrity's formula at the top of p. 125, here, for a function from the set of 2-form fields to the set of tangent vector fields, together with the formula on p. 123 for the exterior derivative of a 1-form field and Theorem 6.3.1 on p. 125 (Garrity: All the Mathematics you...

Homework Statement Let B = {b1, b2, b3} be a basis for a vector space V and T : V -> R2 be a linear transformation with the property that T(x1b1 + x2b2 + x3b3) = 2x1 - 4x2 + 5x3 0x1 - 1x2 + 3x3 Find the matrix for T relative to B and the standard basis for R2. Homework...

Alright, I have a program that converts numbers from base 2-10 and it works just fine but I can not get the program to convert past base 10 whenever i input any char such as 1A it says invalid input. I have tried changing some of the lines in the code but it ends with errors. Right now it is...

Can someone please explain why the representation of a wavefunction as an expansion of basis eigenfunctions actually gives us something of physical meaning? For example, it can tell us the probabilities of measuring a particular eigenvalue (depending on the expansion coefficients)... I mean its...