Bases Definition and 281 Threads

Homework Statement Find a linear transformation T: P_2 \rightarrow M_{22} such that T(1+x)=\left[\begin{array}{cc}1&0\\0&0\end{array}\right] T(x+x^2)=\left[\begin{array}{cc}0&1\\1&0\end{array}\right] T(1+x^2)=\left[\begin{array}{cc}0&0\\0&1\end{array}\right] The Attempt...

Dear all, I have a question concerning Faugere's improved F4 algorithm. You can find it in the attached file faugere_f4.pdf on page 9. In section 2.6 (page 14) an example is given for how the algorithm works. According to the example the second while-loop in the improved F4 algorithm...

Homework Statement does anyone know how i can differentiate a strong acid from a weak acid and likewise for a strong base and a weak base based on its chemical formula? Homework Equations The Attempt at a Solution

Hi There are two things that are confusing me a bit, and was wondering if anyone could explain them. Firstly, if we let V1,V2,...,Vn be vectors in some field F^n and let P = {V1,V2,...,Vn}, then the following are equivalent: (i) {V1,V2,...,Vn} is a basis for F^n ; (ii) P is...

Homework Statement Could someone please explain the difference? Maybe show some examples? Than you! Homework Equations The Attempt at a Solution

I was looking for information in regard to Acids and Bases. I'm having a awful time with conceptual questions concerning this chapter in class, and I'm getting pretty frustrated. Any practice questions / supplemental in depth tutorials would be nice. Thanks!

Homework Statement Hi all. Lets say that we are looking at an operator Q, and two eigenstates given by |1> and |2>. The eigenstates |1> and |2> are not eigenstates of Q, but of some other operator H. My question: Is <1|Q|1>, <1|Q|2>, <2|Q|1> and <2|Q|2> independent of the basis used as long...

Hi there, In 3-dimensional real linear space, the simplest bases can be taken as the canonical bases \hat{x} = \left(\begin{matrix}1 \\ 0 \\ 0\end{matrix}\right), \qquad \hat{y} = \left(\begin{matrix}0 \\ 1 \\0\end{matrix}\right), \qquad \hat{z} = \left(\begin{matrix}0 \\ 0 \\...

I did an experiment with a) strong acid (HCl) and strong base (NaOH) b) weak acid (ethanoic) and strong base (NaOH) so, I am looking at the heat of energy for both the reactions, and so i found that reaction a had a greater heat of energy was that of the reaction b) weak acid and...

Homework Statement Some of the books I have state that the equation of... HCl + NH3 --> NH4+ + Cl- While others state that the above equation should be written as... HCl + NH3 --> NH4Cl Which one is correct? I think the answer should be the second one since the two compounds...

Homework Statement How do you change a base into another number directly without changing to base 10 or base 2 for example? Eg changing 1442 base 6 to base 3 = 112022 Just want to know the steps in the division Teacher wants us to do it this way for less error Help appreciated

Homework Statement This is re-asking the question in https://www.physicsforums.com/showthread.php?t=273275" which mysteriously went quiet before the answer could be given... Anyway I also tried answering the question, but to no avail. Homework Equations a^m.a^n=a^{m+n} (a^m)^n=a^{mn}...

Homework Statement 2-hydroxybenzenediazonium ion is allowed to react with naphthalen-2-ol to form 1-(4-hydroxyphenylazo)-2-naphtholHomework Equations 1.Why is amine having a different solubility in water and dilute hydrochloric acid? 2.Why is naphthalen-2-ol dissolves in sodium hydroxide...

which DNA and RNA bases contain a carbonyl group? Which DNA and RNA bases are primary amines? Thanks for any help

A single particle quantum state \Psi is given a by a wave function (vector) representable as a linear superposition of eigenvectors \Upsilon weighted by a number proportional to their probability of occurrence: \Psi=a_1 \Upsilon_1+a_2 \Upsilon_2+... In the case of the observable "spin"...

Hi How can I work out which subset is a subspace and which one isn't on this problem: Fq ([0,1]) be vector space of all functions [0,1] -> Q with addition and scalar multiplication defined in usual way. Let U < Fq ([0,1]) be the subset consisting of all functions f s.t. f(0) >= f(1) and...

Homework Statement The problem states: Let A_1 = [-1 1] , A_2 = [1 3] ...[0 1]...[-1 0] A_3 = [1 0] , A_4 = [0 -1] ...[1 2]...[2 3] Show that {A_1, A_2, A_3, A_4} is a basis for M_2 R. The attempt at a solution I'm very confused about this problem. I understand that to...

Let T: R3 -> M(2,2) be the linear transformation given by T(x,y,z) = [ z ...-z ] .....[ 0 ... x-y]Fix bases B = {(1,0,0),(0,1,0),(0,0,1)} and C = { [1 0] , [0 1] , [0 0] , [0 0] } ............[0 0]...[0 0]...[1 0]...[0 1]for R3 and M(2,2) respectivelya) Find the matrix [T]c,b of T...

[FONT="Arial"][SIZE="2"]I am probably not phrasing this question precisely enough but ... ... are Number Theorems true regardless of the Number Base? In particular, is any given Number Theorem that is true in Base 10 equally true in Base 2? Thank you. Euan

Homework Statement Show that for any fixed a and b, there is an algorithm to convert an n-digit number from base a to base b with O(n^2) operations. The Attempt at a Solution Really i am completley lost here. Working backwards, i know to convert from base a to a base b you must use...

Homework Statement 4^(x+2)=9 Homework Equations basically all I want to know is what is the best way to go about solving a problem like this. The Attempt at a Solution I know how to convert a problem as such 4^(3x)=10 using. [log(<base>4,10)]/3 = X. however I need some help with...

Hi there I was wondering if anyone could help me with this buffers question ... For which of these liquids is the pH likely to change least if a splash of concentrated sulphuric acid is added? Justify your answer: a) 0.1M hydrochloric acid solution b) 0.08M ethanoic acid/0.02M potassium...

In chemistry it's normal to distinguish between weak and strong acids. Is there a limit for the pKa value that determines what is strong and what is weak? Equivalent, for bases, is there a pKb value that separates weak and strong bases?

In class, I had a question about how to solve the following problem: 6^log6_3 (EDIT: if this is ambiguous without the math formatting, (I don't know how to format it) it reads 6 to the power of log base 6 that yields 3) No one knew how to solve it (including the teacher), and he could...

[SOLVED] Acids, Bases, and Salts I will be starting on a new chapter unit of Acids, Bases, and Salts for class. I was wondering what important information I should be aware of, like equations and laws since I want to stay ahead of my class, and not die if I miss a day.

Homework Statement (a; b) is in terms of D = ( 1,1 ; 1 -1) and (c; d) is in terms of Dx = ( -1,1 ; 0,2), then we need to find a matrix such that (c;d) = (?, ?; ?, ?)* (a; b). Homework Equations y = Ax >> linear transformation The Attempt at a Solution I know the answer is [1, -3...

Homework Statement Like all equilibrium constants, Kw varies somewhat with temperature. Given that Kw is 3.49e-13 at some temperature, compute the pH of a neutral aqueous solution at that temperature. Homework Equations Kw = [H+][OH-] pH = -log[H+] The Attempt at a Solution 3.49e-13 =...

i want to transform a number in base 6 into a number in base 3 i was looking for a way to transform straight forward without any middle man ("from 6 to 10 and from 10 to 3" that's not the way i am looking for)

Homework Statement If I am giving a matrix A representing the linear transformation L(x) = Ax, then A is the matrix-representation of L with respect to the basis elements in the vector-space S (standard). If I am now given another vectorspace V by the matrix V, and I want to find the matrix B...

[SOLVED] Vectors that form bases (linear algebra) Homework Statement I am given two vectors u and v, which are: u = (1/2 , 1/2 , 1/2 , 1/2) and v = (1/2 , 1/2 , -1/2 , -1/2). I have to find an orthonormal basis for R^4 containing u and v. The Attempt at a Solution The first thing...

Homework Statement I have two questions: 1) When I am asked to find the matrix with respect to two bases E and F, that is NOT the same as finding the transition-matrix going from E to F? If not, what does that matrix (with respect to E and F) represent then? 2) If I have a vector-space which...

Homework Statement I have three vectors F, G and H and I want to find the basis for R^5 that contains the three vectors F, G and H. The Attempt at a Solution I write the matrix A <F G H I>, where I is the 5x5 identitymatrix. I bring this matrix to rref, but which columns must I choose...

[SOLVED] Linear algebra; changing bases Homework Statement I have two bases E and F given by: E = [1, x, x^2] F = [1-x, x-x^2, x^2]. I want to find the transition-matrix S that goes from E to F. The Attempt at a Solution To do this, I must write one basis as a linear combination...

I am reading "The linear algebra a beginning graduate student ought to know" by Golan, and I encountered a puzzling statement: Let V be a vector space (not necessarily finitely generated) over a field F. Prove that there exists a bijective function between any two bases of V. Hint: Use...

If for example, I have. Y1=Cos(2Ln(x)) and Y2=Sin(2Ln(x)) and I have to reach the general solution. I know how to get to the general solution is the cauchy equation: y'' X^n + y' x + 4 y = 0 According to the answer, n=2 => y'' X^2 + y' x + 4 y = 0 How am I to know that that it is X^2 ? Or is...

A question about bases I have a question as to why a particular space does not have a countable base. The space is the infinite Cartesian product of the interval [0,1] with the usual topology, with itself.

Homework Statement I have seen two definitions for the topology generated by a basis set: one here http://books.google.com/books?id=9cT2wI-Qrk4C&pg=PA23&dq=basis+for+a+topology&ei=wu3nRua6HYqKoQLlj81v&sig=nNFNyWXorlwCQ8WCwQBDTuI9HUc#PPA22,M1 and the other one is a set U is open if for every...

Homework Statement when a carbonate acts as a base and neutralises an acid, CO2 is formed. the problem is that some of the CO2 dissolves in the water and forms Carbonic Acid.the Carbonic acid will affect the titre value as it will react with the base, along with the HCl. How do we prevent...

Let T: P3 ----> P4 Im attempting to find the matrix for T relative to the bases B and B' T maps P3 to P4 \begin{array}{l} T(ax^3 + bx^2 + cx + d) = (3x + 2)(ax^3 + bx^2 + cx + d) \\ B = \{ x^3 ,x^2 ,x,1\} \\ B^' = \{ x^4 ,x^3 ,x^2 ,x,1\} \\ \end{array}...

What is the difference, if any, between frame fields and coordinate bases?

Hi all. So I'm a bit confused about finding a basis of generalized eigenvectors for an operator that is not diagonalizable. I have some "steps" in mind, but maybe someone can help me out here: 1) Find the eigenvalues of the matrix/operator 2) Find the eigenspaces corresponding to each...

Are these two sets: A = {(0,2,2)^T, (1,0,1)^T, (1,2,1)^T} B= {(1,2,0)^T, (2,0,1)^T, (2,2,0)^T} Bases of V3(R) I have found equations that show that they span V3(R) And that both set are linearly independant. So am I right in saying that they are both bases of V3(R). Cheers Ash

Whilst trying to refresh myself on what a dual space of a vector space is I have confused myself slightly regarding conventions. (I am only bothered about finite dimensional vector spaces.) I know what a vector space, a dual space and a basis of a vector space are but dual bases: I seem...

im looking at some review problems my teacher gave me today, and i can pretty much do most of them. however, there is this one i really have no idea what to do. Its a 2 part problem. 1a.What is the pH of a 1000 ml of a 0.1 M acetic acid solution, given pKa = 4.8? 1b. what is the pH of...

Homework Statement I'm given a subspace in F^5 (not sure how to note that online) and asked to find a basis and dimension for it. I know it should be really easy, but ... Homework Equations We're given subspace W1 = {a1,a2,a3,a4,a5) in F^5: a1-a3-a4=0} . We also know from linear...

Homework Statement find the pH of: 100mL x .20M HOAc + 100mL x.10M Ba(OH)2 The Attempt at a Solution 100x.2 = 20mmol HOAc 100x.1 = 10mmol Ba(OH)2 20-10=10 10/200=.05M pOH = -log(.05) = 1.3 pH=14-1.3=12.7 Is this correct?

Anyone clever with bronsted acids and bases? I'm pretty new in chemistry, but I'm trying to learn. Right now I'm suppose to classify some species as either bronsted acids or bases, or even both. For example 1. Water 2. OH- 3. NH4+ 4. HCN 5. HBr 6. NH3 Hope someone can help...

I'm having trouble understanding bases outside of R^n; I've got a handle on those I think. Here are some examples: 13. In C(-Pi,Pi), find the dimension of the subspace spanned by 1, cos(2x), and cos^2(x). 14. Find the dimension of the subspace of P3 spanned by x, x-1 , x^2+1, x^2-1...

I am a little stuck on this question : Solution A contains n moles of a weak acid HX. The addition of some sodium hydroxide to A neutralises one third of the HX present to produce Solution B. In terms of the amount, n how many moles of HX are present in Solution B? I think there are one...

What principle explains the solubility of a substance in aqueous acid or aqueous base? Ionic solutes and its dissociation is involved in a substance's solubility in an aqueous acid or base. This solubility can be expressed by a chemical equation in which a basic salt results when a a weak...