Algebra Definition and 999 Threads

Homework Statement Construct a subset of the x-y plane R2 that is (a) closed under vector addition and subtraction, but not scalar multiplication. Hint: Starting with u and v, add and subtract for (a). Try cu and cv Homework Equations vector addition, subtraction and multiplication The...

This is a linear algebra question which I am confused. 1. Homework Statement Prove that "if the union of two subspaces of ##V## is a subspace of ##V##, then one of the subspaces is contained in the other". The Attempt at a Solution Suppose ##U##, ##W## are subspaces of ##V##. ##U \cup W##...

Homework Statement define the time in an analog clock up to the second. The time needs to be such that the minute hand, is at the exact same position as the hour hand. This position of the hands needs to be between 10th and 11th hour. Homework Equations 3. The Attempt at a Solution [/B] I...

Homework Statement The Attempt at a Solution \left[ \begin{array}{cccc} 1 & 0 & 5 & 2 \\ -2 & 1 & -6 & -1 \\ 0 & 2 & 8 & 6 \end{array} \right] \sim \left[ \begin{array}{cccc} 1 & 0 & 5 & 2 \\ 0 & 1 & 4 & 3 \\ 0 & 0 & 0 & 0 \end{array} \right] From the RREF it is...

the answer key said d is supposed to be 10. but there's a way to evade that row exchange. 1st picture is the question and the 2nd picture is the elimination steps.

Ok so a bit of background about myself I finished 1. Algebra 1 and 2 2. Trigonometry (Basics) 3. Basics of complex numbers 4. The very basics of matrices (addition, subtraction, multiplication, identites, inverses only) 5. Basic differential Calculus I want to learn mathematics in this order...

I am asking this question as I have found Boolean Algebra quite intriguing. I have a good understanding of high school level probability and statistics and also Algebra II. Is this enough or do I need more "mathematical maturity"? Anyway, thank you in advance.

Hello! I just started reading about SU(2) (the book is Lie Algebras in Particle Physics by Howard Georgi) and I am confused about something - I attached a screenshot of those parts. So, for what I understood by now, the SU(2) are 2x2 matrices whose generators are Pauli matrices and they act on a...

Hello! I am sorry that this questions is not actually directly related to physics, but, can anyone recommend me a good book about abstract algebra (basically lie algebra, representation theory etc.) used in physics? I have tried for a long time to find something online but I haven't find a...

Hi! I would like to know if my solution for this inequality is corect or not:

Homework Statement Note: I'm saying it's very very hard because I still couldn't solve it and I've posted it in stackexchange and no answer till now. I'm posting here the problem statement, all variables and known data in addition to my solving attempts. Because I'm posting an image of my...

hi! i need help for this inequality 1. ##a\in\mathbb{N}*~and~ \frac{a}{a+1}<\frac{a+1}{a+2}<\frac{a+2}{a+3}## show that : ##\frac{1}{2}*\frac{4}{5}*...*\frac{2005}{2006}*\frac{2008}{2009}<\frac{1}{12}## Here i have stoped. Please tell me if is corect what i have done so far and how to continue ...

Homework Statement Consider the four vectors (1, 1, 1), (2, −1, 3), (1, 7, −1) and (1, 4, 0). Calculate how many ways you can write (1, 1, 1) as a linear combination of the other three, explaining your reasoning. The Attempt at a Solution wouldn't any of these combinations give the correct...

Homework Statement (A OR C) AND NOT(C AND A AND B OR C AND A AND NOT B) or (A + C) (CAB + CAB')' Relevant Equations (A+B)' = A'B' A(B+C) = (AB) + (AC) (AB)' = A' + B' The attempt at a solution I'm not sure how I'm suppose to expand (CAB + CAB')' for simplifying. I keep arriving at false which...

Given that $$a,\,b\in\Bbb{N}$$ such that $$\sqrt{a^2+2b+1}+\sqrt[3]{b^3+3a^2+3a+1}$$ is a rational number. Find the relationship between $a$ and $b$.

The problem statement: Show that if ##r_1## and ##r_2## are the distinct real roots of ##x^2 + px + 8 = 0##, then ##r_1 + r_2 > 4 \sqrt{2}##. We start by noting that ##r_1 r_2 = 8##. Using this relation, we'll find the minimum value of ##r_1 + r_2##. To minimize ##r_1 + r_2##, we need to...

Hello, I just completed a first course in linear algebra and really enjoyed my studies. So much so that I want to pursue it more in the fall as an independent study, i am a EE major in college and was curious what directions might be useful for applications in that field.

Dear Physics Forums friends, I am an aspiring mathematician who is deeply interested in the analysis, topology, and their applications to the microbiology. Recently, I started to become very curious about why concepts and theorems in the real analysis and topics come as they are; the...

Is there a website that anyone can suggest to practice Algebra, and/ or Calculus?

Question 1: Consider the numbers 2 & 8. The average between these two quantities is 5, hence 2+8=10, 10/2=5. Now consider two arbitrary derivatives. It wouldn't make much sense to find the average between two unrelated derivatives, but suppose that f(x,y) was a function of both x & y. Now...

Homework Statement I did some refresher exercises in khan academy. I tried to wrap my head around the factoring problems, but it did not go well... I did not understand the khan academy tips and hints. (about factoring) one particular difficult polynomial was thus: factorize the polynomial...

Homework Statement Homework Equations a) the one given b) det(A-λI) = 0 find λ values using A c)use λ values to find eigenvectors The Attempt at a Solution This wasn't explained well enough so I can understand it in class. So far, I made the matrix being multiplied to A have the following...

Homework Statement Prove Rθ+φ =Rθ+Rφ Where Rθ is equal to the 2x2 rotational matrix [cos(θ) sin(θ), -sin(θ) cos(θ)] Homework Equations I am having a hard time trying figure our what is being asked. My question is can anyone put this into words? I am having trouble understanding what the phi...

Homework Statement Let P2 be the vector space of all polynomials of a degree at most 2 with real coefficients. Let T: P2→ℝ be the functioned defined by: ##T(p(t)) = p(2) - p(1)## a) Find a non-zero element of the Kernel of T. (I think I figured this one out, but I'm not too sure). b) Find a...

Hey everyone, I understand how to normalize a second order system, but I wanted to know if the same steps are taken when the parameters of the system are not scalar but matrices. For example where the parameter phi, and gamma are both 3x3 matrices and X is a 3x1 vector. From what I've see...

Hello from Italy I'm switching from CS to Physics BS because i personally find it more various and interesting (and in Rome there is one of the best physics school in the world). Mathematical analysis is a common subject and my credits will be recognised but i didn't study Linear algebra yet...

Homework Statement Homework Equations Quadratic discriminant The Attempt at a Solution I did b^2 -4ac>=0, but the algebra becomes prohibitively difficult.

I am trying to learn Geometric Algebra from the textbook by Doran and Lasenby. They claim in chapter 4 that the geometric product ab between two vectors a and b is defined according to the axioms i) associativity: (ab)c = a(bc) = abc ii) distributive over addition: a(b+c) = ab+ac iii) The...

The determinant of some rank 2 tensor can be expressed via the exterior product. $$T = \sum \mathbf{v}_i \otimes \mathbf{e}_i \;\;\; \text{or}\sum \mathbf{v}_i \otimes \mathbf{e}^T_i $$ $$ \mathbf{v}_1\wedge \dots \wedge \mathbf{v}_N = det(T) \;\mathbf{e}_1\wedge \dots \wedge\mathbf{e}_N$$ The...

What are good books in universal algebra, given that I have a background in Herstein (Topics in Algebra), Hubbard/Hubbard, Engelking (Topology), and Dugundji (Topology)? I am currently reading Hungerford, and I found a field called universal algebra while searching internet for some concepts...

Prove that $m^5+3m^4n-5m^3n^2-15m^2n^3+4mn^4+12n^5$ is never equal to 33.

Hi all, Just curious on whether temporal databases are designed in the same way as "standard" relational databases, so that queries on temporal databases are wffs in temporal logic , i.e., using Until, Release and all other unary operators , and the query outputs is the set of models for the...

Hi As the title suggests, I'm looking for a math book that has some competition-style problems in it, with explanations on how to solve them. I have found numerous of other competitions online but the explanations are very not understandable for me. I am NOT talking about international...

Homework Statement 1. How did they complete the square for these equations in the picture below? What was their thought process? 2. distance/velocity = time , velocity/acceleration = time , In leibniz notation how does this cancel out? When you divide, how does it cancel out to give you a...

micromass submitted a new PF Insights post How to self-study algebra. Part II: Abstract Algebra https://www.physicsforums.com/insights/wp-content/uploads/2016/06/aastock6.png Continue reading the Original PF Insights Post.

Homework Statement If n is a positive integer, then 2x2 matrix [-32,252] [-4,32] raised to the power of n is... Homework Equations I know that first I should diagonalize the given matrix, something I also seem to have a hard time with. The Attempt at a Solution I determined the eigenvalues...

So I've always been fairly good at whatever science I learned in elementary and middleschool (which was mostly biology), and I've fairly enjoyed it, but I've only recently started really learning, and I've come to love it. I've especially found quantum physics interesting, however, seeing as I...

Homework Statement Find the matrix that represents a rotation counterclockwise around the origin by 75 degrees followed by a reflection about the x-axis Homework Equations I know that for A rotated counter clockwise you use the 2x2 matirx [cos(theta), -sin(theta)] [sin(theta, cos(theta)] and...

Hi everyone, didn't know where to post question on sigma algebra so here it is:- What I've tried till now: Let $$C\in G$$ 1) For $$C=X, f^{-1}(B)=X$$ which will be true for $$B=Y$$ (by definition) 2) For closure under complementation, to show $$C^{c}\in G. So, C^{c}=X\setminus C=X\setminus...

Current schedule: Summer: Elective Fall: -not important, but it can't be changed in any way- Spring: Differential Eqs., Classical Mechanics & Mathematical Methods 1 (Physics), Linear Algebra, Chemistry Lab, Elective I'm thinking that since the spring schedule looks kinda heavy I can switch up...

Homework Statement The period of a simple pendulum, defined as the time necessary for one complete oscillation, is measured in time units and is given by T = 2π ℓ/g where ℓ is the length of the pendulum and g is the acceleration due to gravity, in units of length divided by time squared. Show...

i am trying to divide x^3+(1-k^2)x+k by (x+k) but i can't do this can you show me how to.

I am reading through a introductory algebra textbook and refreshing memory on this topic. In the matter of the Associative Properties, it is giving me the expression 3 + (8+x). (I'm skipping the graphs section because I'm leaving that for my tutor Saturday. But I'm moving to algebra because I...

I am reading Dummit and Foote's book "Abstract Algebra" (3rd Edition) and am focused on Chapter 15: Commutative Rings and Algebraic Geometry ... ... On page 657 D&F give a definition of a k-algebra ... as follows: I have to say I do not find that this definition gives me a good intuitive idea...

I am reading Dummit and Foote's book "Abstract Algebra" (3rd Edition) and am focused on Chapter 15: Commutative Rings and Algebraic Geometry ... ... On page 657 D&F give a definition of a k-algebra ... as follows:I have to say I do not find that this definition gives me a good intuitive idea...

Factorize $x^4+y^4+z^4-xyz(x+y+z)$.

Hello! Please help continue solving tye problem I got stuck. This is my attemptlet $d=$ length of the circuit $\frac{60}{a}$mph --- speed for walking $\frac{60}{b}$mph ----speed for riding $\frac{60}{c}$mph ---- speed for driving $d = \frac{60}{a}t_{1}+ \frac{60}{b}t_{2} + \frac{60}{c}t_{3}$...

Homework Statement Homework Equations I can't start because I did not understand the statement in red underline. Please explain to me first. Then I may be able to solve it. Sorry english is not my first language. Hope you would understand. Thank you! The Attempt at a Solution

Hello! I am a diploma student at HEP section. I am going to have an interview for PhD within a week. I've finished the course and learned a lot about Lie algebra, quantum field theory, general relativity, standard model, etc. How can I review everything as soon as possible? For example, Mark...

I want to prove: $$A\cup B=A\cap B\Longleftrightarrow A=B$$ Forall A,B sets By using the axioms and theorems of the Boolean Algebra. Any hints ??