Bases Definition and 281 Threads

If I had a nucleophile, say the conjugate base of benzene, and a molecule with a bromide, and a primary alcohol. Would the nucleophile attack the carbon bound to the bromide, or the proton on the alcohol? If it's hard to follow I can try to make a picture. Basically I want to add Isobutanol...

Homework Statement Let G be a Lie group and L be its Lie algebra. Further assume that TG is equiped with a metric tensor g; that is, a (0,2)-covariant tensor that is symmetric and positive-definite on fibres of TG. Assume that \{ H_i\}_{i=1}^m are an orthonormal basis for for L. If R_X: G...

Homework Statement Find bases for the following subspaces of F^5: W1 = {(a1, a2, a3, a4, a5) E F^5 : a1 - a3 - a4 = 0} and W2 = {(a1, a2, a3, a4, a5) E F^5: a2 = a3 = a4 and a1 + a5 = 0} 2. The attempt at a solution Well, I understand a basis is the maximum amount of vectors...

I have a Topology midterm tomorrow and I'm going through exercises in my book. Perhaps someone could let me know whether I ought to make a thread for each question or if I may continue adding to this thread... Determine which of the following collections of subsets of R are bases: a.) C1 =...

So, it's for Mastering Chemistry and I need to sort out the strong acids weak acids strong bases and weak bases. It says that two are wrong though I've looked them all up and don't know which ones are wrong. [PLAIN]http://bit.ly/fREfFS

Say I was given a 2x2 matrix made from a certain basis {|x\rangle, |y\rangle} , and I split that matrix into two parts, one being the diagonal part and one being the off-diagonal part. for example, if I had H = H_0 + W = \left(\begin{array}{cc}a&c\\b&d\end{array}\right) =...

If we have a vector that can be expressed in terms of some finite list of basis elements. If we have an orthonormal basis for a vector space V, then a vector v can be expressed as <v,e1>e1 +...+ <v,en>en. This appears to be widely used for many results (such as Gram-Schmidt), but the...

Find bases for the kernal of the following: T(x1,x2,x3,x4) = (x1+x2+x3,-x3,x1+x2) Any help would be great thank you

Homework Statement V is a subspace of Rn and S={v1,...,vk} is a set of linearly independent vector in V. I have to prove that any list of linearly independent vectors can be extended to a basis for V. Homework Equations None that I can think of. The Attempt at a Solution So to be...

I need some help with developing an idea for my design lab. it is a lab where we must come up iwth a problem to solve on our own. This time we are to discover something new about acids and bases. What would be a good problem? thank you!

Can anyone explain to me how to determine whether a compound is a strong acid, weak acid, strong base, weak base, or amphoteric? Thanks!

hi, i wonder if there is any clear chemical difference between the bases pairs CG and AT? is one more reactive than the other one for example? is there any chemical difference that is used? i would be very grateful for any reply! thanks!

Homework Statement Let U be a subspace of R4 and let S={x1, x2, x3} be an orthogonal basis of U. Given x1, x2, x3, find a basis for Uperp (the subspace containing all vectors orthogonal to all vectors in U). I am actually given three vectors x1, x2, x3, but I am looking more to...

hi, anyone can enlighten me why the pauli x matrix in the z basis is given as 0 1 1 0 while it in the x basis, it is given as 1 0 0 -1 is there a formula or something to calculate this? and how does one know that a matrix is in the z basis or the x basis? thanks a lot!

Homework Statement I have posted this problem on another website (mathhelpforum) but have received no replies. I don't know whether this is because no one knows what I am talking about or if it's just that no one can find a fault with my reasoning. Please please please could you post a reply...

I'm trying to get a handle on these concepts, which are new to me. http://planetmath.org/encyclopedia/HamelBasis.html : Kreyszig offers the following example of a Schauder basis for l^2: e_i=(\delta_{ij}) (Introductory Functional Analysis with Applications, p. 43-44). Since any vector can...

This is a subject I am unfamiliar with, and was just wondering where I should start in order to learn about them and how they affect different elements and form other substances step-by-step. From what I know, an Acid donated a Hydrogen Ion, and a Base takes a Hydrogen Ion, and an Acid has to...

Homework Statement Calculate (5^7)-(7^7)+(9^7)-(11^7) in Mod24 Homework Equations The Attempt at a Solution I added all the bases and got -4 (which I changed to 4), then I took 4^7 and ended up with 16,384. I divided 16,384 by 24 as many times as I could, which gave me an end...

Homework Statement I'm a little confused, let's say i do a titration curve for a weak acid, at some point there's a buffering range near the pKa. Like i know that if we add a strong base like NaOH to acetic acid in a water solvent, then the OH- will combine with the H+ (hydronium ion) which...

Find the integral ∫(3^(2x))/(1 + 3^(2x)) dx so I have that u= 1+3^(2x) and du=2ln3[3^(2x)] I=1/(2ln3)∫3^(2x)(2)(ln3)/(1 + 3^(2x)) dx Can anyone help me solve this please?

Homework Statement 9 log3(2x+1) + 4 log2(x+3) = 85. Find x! Homework Equations logarithm The Attempt at a Solution I have tried few things but useless. Do not know what to do with different bases. I also tried to change the RHS: 85 = 5 x 17 but nothing worked. Thank you very much

Homework Statement I'm working on the problems attached. Homework Equations The Attempt at a Solution I think I understand how to do problem 4.3 but I'm lost on 4.1 and 4.2, and I'm pretty sure i need to figure those out before I can do 4.3. Can someone please try to guide...

Homework Statement How do I find the bases for both the kernel and range of this linear transformation? Let T: R4 ----> R4 be the linear transformation that takes [1101] and [1011] to [2304] and takes [1110] and [0111] to [3120] a. Find the bases for both the kernel and the range of...

I was working on a problem earlier today and I didn't know the following result: Let S be a subset of an infinite-dimensional vector space V. Then S is a basis for V if and only if for each nonzero vector v in V, there exists unique vectors u1,u2,...,un in S and unique nonzero scalars...

Yet another question about the evolution of life, likely in the Archaen or Proterozoic eons. As I understand it, the genomes of all life - archaea, bacteria, eukaryotes - is based on DNA, even that of eukaryote organelles, such as plastids and mitochondria. Are there any counter-examples, in...

I'm a beginner at differential geometry. I have a problem about dual space. I understand why we use \left\{\frac{\partial}{\partial x^{\mu}}\right\} as the bases in vector space, but I have no idea why we use \left\{ dx^{\mu} \right\} as the bases of dual space. What is the reason of...

Homework Statement Let T be the linear transformation T: M2x2-->M2x2 given by T([a,b;c,d]) = [a,b;c,d][0,0;1,1] = [b,b;d,d] Find bases (consisting of 2x2 matrices) for the image of T and the nullspace of T. Homework Equations Standard basis of a 2x2 matrix...

Hi: Given a fin.dim vector space V over R, and two different bases B_V,B_V' for V , we say that B_V,B'_V are equivalent as bases ( or have the same orientation) , if there exists a matrix T with TB=B', and DetT>0. How do we define equivalent bases for vector spaces over the...

Homework Statement Prove that all bases for subspace V of R\hat{}N contain the same number of elements. Homework Equations The Attempt at a Solution I have absolutely no idea where to start this proof. Do I need to do something with finding an equation of the subspace, or not?

I'm just learning linear algebra, where we are taking a set of basis vectors and then using gram schmidt to convert them to an orthonormal basis. So I know I can do it. I know orthonormal is great. But as I'm modifying the basis anyway from the original, why don't I just forget the original...

I have been playing around with numbers in different bases and then I thought, what if they were in fractional bases. I found a way to convert numbers to fractional bases and have been searching on the internet and not found a similar way to do this. Anyway, here is an example of how I would do...

Given a set of n<d commuting operators, either degenerate or non-degenerate, in a d-dimensional Hilbert space, is there an effective analytical method of finding an orthonormal basis composed of d eigenvectors common to all the operators in the set? The operators are dxd complex square matrices...

Hi, again another problem: Let B1 = {( \stackrel{1}{3}),( \stackrel{1}{2})} and B_{2} = [ \frac{1}{\sqrt{2}}( \stackrel{1}{1}), \frac{1}{\sqrt{2}} (\stackrel{-1}{1}) ] Determine the representing matrix T = K_{B_{2},B_{1}} \in \Re^{2\times2} for the change from B1 coordinates to...

Homework Statement Indicate the conjugate bases of the following: NH2- NH2- Homework Equations The Attempt at a Solution This is the only information given. Can I assume that these species react with water? The ionic signs indicate that they are bases, but are they the...

Not sure where this should go, but - How would you calculate the square root of a triangular number with a base other than 1? For example, 2, 6, 12, 20 (Base 2). Would rather have help to figure it out than the actual formula.

Homework Statement So I'm trying to find a basis for the space that is spanned by the given vectors. {(1,0,0,1) (-2,1,-1,1) (6,-1,2,-1) (5,-3,3,-4) (0,3,-1,1)} These are written as column vectors. Homework Equations None really (that I know of) The Attempt at a Solution So I...

Homework Statement Let T be the linear transformation of R5 into R3 that has the matrix A = 1 3 2 0 -1 2 6 4 6 4 1 3 2 2 1 relative to the bases [(1,1,1,1,1), (1,1,1,1,0), (1,1,0,0,0), (1,0,0,0,0), (0,0,0,0,1)] of R5 and [(1,1,1), (0,1,0), (1,0,0)] of R3. Find a basis for the range...

I'm having some trouble understanding basis and how they relate to transformation matrices. Homework Statement Let e_1,e_2,e_3,e_4 be a basis in a four dimensional vector space V. Suppose that the linear transformation F on V has the matrix representation: [1 0 2 1;-1 2 1 3;1 2 5 5;2 -2 1...

Homework Statement Only the equation: 2(3^x) = 7(5^x) Homework Equations N/A The Attempt at a Solution Okay. I've been fine learning the loglaws, until I hit this question. If they were the same base (or at least near the same, ex: 2 & 8) then I could simply change them into...

Homework Statement I was asked to calculate the pH of .40M solution of NH4ClO4 but I wasn't given a Ka for it. Homework Equations The Attempt at a Solution I dissciated NH4ClO4 into: NH4(plus) and ClO4(minus) but I"m stuck there. What am I doing wrong?

hi, this is my first post on this site so please excuse me (and correct me) if i am not posting according to the guidelines. im studying right now linear transformations and I am a bit shaky concerning dual vector spaces. i understand the definition but am not sure how to apply it. what...

How would you solve a problem like this where you have to find what base A is for this equation to be true? So in what base are these numbers.24)A + 17)A = 40)A Not asking the answer for this particular question but how you'd solve it (other than trial and error obviously)

Homework Statement You prepared a reaction table for 10.0 mL of 0.1 M NH4Cl with 5.0 mL of 0.1 M NaOH. Please choose all of the following that describe the solution that was produced. The choices are: 1. a solution containing only a strong base 2. a solution containing a weak acid and a...

Hey, I just got out of my lab at school and just realized that me and my professor made a mistake. He marked my lab complete, and I also thought it was complete, however, I just realized that there was something missing. The problem is that I can't go back into the lab to try it out again...

The pKa for the dissociation of H3PO4 is 2.15. What is the concentration of H2PO4-1 (in M) at pH 3.21 if the original concentration of the phosphate was 2.37 M? My Attempt: Key Information: pH final: 3.21 Initial Molarity of phosphate: 2.37 M pKa: 2.15 I started with the first...

Hi ! I am a little bit confused with notation in the following: Let A= \begin{bmatrix} 2 & 3 & 4 \\ 8 & 5 & 1 \\ \end{bmatrix} and consider A as a linear transformation mapping \mathbb{R}^3 to \mathbb{R}^2. Find the matix representation of A with respect to the bases...

Here's the question: And the answer is: Which makes sense to me, because acetic acid is the stronger acid. But there's another option in the list that it says is NOT true: I thought this might be true, because both are solutions of chemicals that were referred to as acids. Am I...

Does anyone know if its possible to check whether a number is a perfect square in 2 different bases ? ( I don't mean the representation of a number in 2 different bases - coz that would be a ridiculous question , what I mean is consider a no say xyz - is it possible to prove / disprove that it...

If you measure the position of an elementary particle exactly, then its position becomes unknown. So consecutive measurements of position do not give the same result. There's been some recent papers by G. Svetlichny, J. Tolar, and G. Chadzitaskos that show that position measurements move around...

hey guys, i have a question, then i will show my solution, is there any chance you guys could help me find an easier way to get to the answer, cheers question: log_3 3x answer: log_a (yx) = log_a (y) + log_a (x) log_3 (3) + log_3 (x) log_a (y) = x -> y = a^x -> log_a (a) = 1...