Algebra Definition and 999 Threads

https://scontent-mxp1-1.xx.fbcdn.net/v/t35.0-12/13324008_10209600482268675_3779883_o.png?oh=abd4c815b9472f70cfbfbb1923a37b3c&oe=5752F454 Number 12 : I have simplified it and I have got AB but the model answer in red say A(comp(B)+c) I just want is that answer true or not , thanks in advance

MENTOR NOTE: Moved here from the General Math forum hence no homework template. Hello! Sorry for not showing what I have tried to solve the problem. Here it is I let x = amount of inferior tea to be added to superior tea in lbs. y = amount of superior tea in lbs. 3x+5y = 11/3(x+y)...

##\nabla p = \rho \nabla \phi ## My textbook says that by taking the curl we get: ## 0=\nabla \rho X \nabla \phi ## ** I don't follow. I understand the LHS is zero, by taking the curl of a divergence. But I'm unsure as to how we get it into this form, from which it is clear that the gradients...

Homework Statement Under what restrictions on ##c, d, e##, will the combinations ##c\vec u + d\vec v + e\vec w## fill in the dashed triangle? Homework Equations The Attempt at a Solution Clearly, ##\vec w + a (\vec v - \vec w) + b(\vec u - \vec v)## will be in the triangle when ##0 \leq b...

I'm trying to better understand RSA and Diffie-Hellman exchange and the modulus math that they are base on, there are some questions I have about there properties for which I am unable to find concise explanations about. I'm generally interested in how the commutative, associative...

Homework Statement son and father and granpa have same value for their birthday (except the year ostensibly) father is nine times the son's age now. calculate the granpa's age now. clues - five years ago, grandpa was 32 years older than what the father was at five years ago. -in five years...

Homework Statement cellphones are sold at price of 302$ per unit In one week there were 450 units sold. for every one dollar increase in unit price, the weekly sales of the phones fell by four units. form a function which describes the weekly sales income when the phone's price changes by X...

Homework Statement a memory stick was sold with 3 $ discount seven discounted memory sticks costed 12 dollars more than five of the non-discounted-memory sticks what is the price of non-discounted memory stick (normal price if you will) Homework EquationsThe Attempt at a Solution This is...

http://arxiv.org/abs/1001.2485 --- The above paper is about a possible two-time formulation of physics. It is by serious people. To understand it I'm trying to generalized the Dirac eqn. to 3+2 dimensions with signature (++---) I found the following (now closed post) useful...

I was wondering if there was anyone comfortable enough about basic to advanced linear algebra concepts who would be willing to participate in a chat/whiteboard based platform to discuss or answer questions concerning such concepts. I need clarification on a few things

Homework Statement If ##a+\frac{1}{a}=\sqrt{3}##, then ##a^{2016} + (\frac{1}{a})^{2016} ## equals A. 0 B. 1 C. √2 D. √3 E. 2 Homework EquationsThe Attempt at a Solution [/B] I find no real solution for a. What I can do is just find a^2 + (1/a)^2 which equals 1, a^4 + (1/a)^4 = -1, a^8 +...

I've been learning algebra for the past 2 years (in high school), not once have we ever had to rationalize a denominator in a radical expression. I am now relearning Algebra and Trig., what use is there? I mean, all you're doing is switching the numerator (rational) to the Denominator...

Homework Statement I am watching a course on Relativistic Quantum Mechanics to freshen up, and I have found to have some issues regarding simple operator algebra. This particular issue on the Pauli Equation (generalization of the Schrodinger equation that includes spin corrections) in an...

Homework Statement Prove the following: Let V be a vector space and assume there is an integer n such that if (v1, . . . , vk) is a linearly independent sequence from V then k ≤ n. Prove is (v1, . . . , vk) is a maximal linearly independent sequence from V then (v1, . . . , vk) spans V and is...

Homework Statement Prove the following theorem: Let (v1, . . . , vk) be a sequence of vectors from a vector space V . Prove that the sequence if linearly dependent if and only if for some j, 1 ≤ j ≤ k, vj is a linear combination of (v1, . . . , vk) − (vj ). Homework EquationsThe Attempt at a...

Computer science major here. I recently completed calculus I, II, III. Now I know that I'll probably be required to take linear algebra. So far, I expect to do some Gaussian elimination (assuming I know what a row echelon is). What else should I expect from linear algebra?

Hello. I am a sophomore and I attend an Early College High school. I am currently in Geometry this year and I will be taking Algebra II during the first half of summer. To account for the second half-credit of Algebra II, I will be taking College Algebra in the second half of summer. Throughout...

I'm having trouble getting started on this one and I'd really appreciate some hints. This question comes from Macdonald's Linear and Geometric Algebra book that I'm using for self study, problem 2.2.4. Homework Statement Let U1 and U2 be subspaces of a vector space V. Let U be the set of all...

Homework Statement Solve the equation for r,r>0,r<R. \frac{-2\pi R^3}{3}-\frac{8\pi r^2\sqrt{R^2-r^2}}{3}+2r^2R+\frac{2\pi}{3}R^2\sqrt{R^2-r^2}=\frac{2\pi R^3}{3} 2. The attempt at a solution After factoring, -2R(2\pi R^2-3r^2)=2\pi\sqrt{R^2-r^2}(4r^2-R^2). After squaring, 64\pi^2...

In the case of two fields interfering with each other when calculating the total electric field, cos (phi1-phi2 + kx) = cos( kx) where kx is the path difference between the two fields. How does cos (phi1-phi2 +kx)=cos(kx) Isit just algebra?

Homework Statement Find the SVD of Homework EquationsThe Attempt at a Solution I'm stuck My question is why in the solution it originally finds u_2=[1/5,-2/5]' but then says u_2=[1/sqrt(5),-2/sqrt(5)]'. I don't see what math was done in the solution to change the denominator from 5...

Homework Statement Simplify the expression ##cb' + ca'b + cabd + cad'## Homework Equations All the properties of boolean algebra. The Attempt at a Solution Here's how I did it: $$cb' + ca'b + cabd + cad' = $$ $$c(b' + a'b + abd + ad') = $$ $$c(b' + a'b + a(bd + d')) = $$ $$c((a + a')b' + a'b...

I'm reading Gelfand's algebra, and I encountered some wonky stuff that I can't figure out on my own (hence my need for the book in the first place) in problem 42 of the book. Here is an explicit statement of the problem. I thought parts a. and b. were easy, but when it came to part c., I just...

micromass submitted a new PF Insights post How to Self-study Algebra: Linear Algebra Continue reading the Original PF Insights Post.

I am reading Bruce N. Coopersteins book: Advanced Linear Algebra (Second Edition) ... ... I am focused on Section 10.3 The Tensor Algebra ... ... I need help in order to get a basic understanding of Example 10.1 in Section 10.3 ...Example 10.1 plus some preliminary definitions reads as...

I am reading Bruce N. Coopersteins book: Advanced Linear Algebra (Second Edition) ... ... I am focused on Section 10.3 The Tensor Algebra ... ... I need help in order to get a basic understanding of Definition 10.5 in Section 10.3 ...Definition 10.5 plus some preliminary definitions reads as...

Hello, As you might discern from previous posts, I have been teaching myself: Calculus on manifolds Differential forms Lie Algebra, Group Push forward, pull back. I am an engineer approaching this late in life and with a deficient background in math. It is all coming together and I almost...

https://www.math.ucdavis.edu/~anne/linear_algebra/

I know the arrow -> means a map. For example, defines a linear map. But I cannot figure out what does a X mean? I know that above denote a inner product map. whatever is on the left of the : is defined by whatever is on the right. but what is the x symbol? What is the correct way to read...

Homework Statement Let A be an n×n matrix which has the property that A^2 =A. (i) Write down the most general polynomial in AHomework EquationsThe Attempt at a Solution My biggest problem is that I don't even understand what the question is asking Is it just sum (alphaA^n)=0 but A^n=A...

Homework Statement Let(v1, v2, v3) be three linearly independent vectors in a vector space V. Is the set {v1-v2, v2-v3, v3-v1} linearly dependent or independent? Homework Equations Linearly independent is when c1v1+c2v2+...+ckvk=0 and c1=c2=...ck=0 The Attempt at a Solution c1(v1-v2)+...

Homework Statement I'm told to find the matrix Q of the matrix A Homework EquationsThe Attempt at a Solution So my problem is that in the answer key they have S = (1/3)... and I have no idea where this 1/3 comes from. I get an equivalent answer for X_1, X_2, and X_3 S = [X_1, X_2, X_3] but...

which has higher failure rate: linear algebra or intro to programming. I understand failure rate might be skewed: math majors, who are gifted and interested in math, are required to take linear algebra but not intro to programming, while CS majors are required to take both. Which class do CS...

Homework Statement [/B] Th value of 'a' for which the equation x3+ax+1=0 and x4+ax+1=0 have a common root is?Homework EquationsThe Attempt at a Solution i initially thought of subtracting both the equations and then finding x and substituting back in the equation but it did not work.

It is a bit of a long question about series, But what is important is this... a+ 2c = 3b (3b-2)^2 = 2a * (4c-2) It is asking for the ratio c to a It have tried a lot of ways. I always end up with this. (Note maybe I not noticing a mistake, Can just anyone confirm that this is solvable? )...

Homework Statement Let R2 have the Euclidean inner product and use the Gram-Schmidt process to transform the basis {u1,u2} into an orthonormal basis. u1 = (1,-3) u2 = (2,2) Homework Equations Gram-Schmidt process: \\v_1 = u_1 \\v_2= u_2 - \frac{\left ( \left \langle u_2, v_1\right \rangle...

where ##□=\nabla^{\mu}\nabla_{\mu}## is the covariant D'Alembertian. ##□x^{\mu}=0## ##g^{\rho\sigma}\partial_{\rho}\partial_{\sigma}x^{\mu}-g^{\rho\sigma}T^{\lambda}_{\rho\sigma}\partial_{\lambda}x^{\mu}=0## So this line is fine by subbing in the covariant derivative definition and lowering...

Homework Statement I'm trying to solve this circuit when I try to simulate and run a dc sweep i get that it can't be solved. When I try to find the answer using linear algebra I get this answer after I throw it into MATLAB with the warning “[w]arning: Matrix is close to singular or...

Homework Statement I feel like I should know the answer to this, so I believe this to be an easy question. Say have matrix A, and I store the elimination matrices E_1,1 E_2,1 etc. and somewhere in the elimination process I have to use a permutation matrix to swap rows. My question is when I...

I am reading in my group theory book the well known commutation relations of the Lie algebra of SO(3), i.e. [J,J]=i\epsilon J. What I don't understand is the statement that "from the relations we can infer that the algebra has rank 1". Any ideas?

Homework Statement So I think I found an error in the solution were it attempts to find q_2^ I'm asked find the orthornomal basis for the column space of matrix A. Homework EquationsThe Attempt at a Solution [/B] My question is in what it puts for q_2^ A_2 = [4/3 4/3 -2/3]^T ||A_2|| =...

Homework Statement A line is given by the equation ##x + 2y - 3z = 7##. Find any vector in the direction parallel to this line in the Cartesian coordinate system. Homework Equations I imagine that there are some fundamental relationships I am missing here that would make this more...

Homework Statement I feel like this is a easy question but it seems the answer key doesn't seem to be right. So say I have 2 vectors and I'm trying to find the projection of vector u perpendicular to the vector v Homework EquationsThe Attempt at a Solution So I don't remember doing...

Homework Statement I ask for help in solving the exercises in this project on applied linear algebra. The problem outlined in the project is one in which we are tasked with modeling the demise of a gambler. I need help solving exercise 1 (in red) on page 6. I have pasted the exercise text...

Homework Statement So yeah I'm doing a project were I get to create a problem. I would like to learn how to solve a AC RLC circuit using linear algebra. I'm trying to find all of the currents on the edges of the graphs and find all of the voltages at the nodes connecting the edges. I don't...

Homework Statement I got following Question from a book: I am doing it using a different method but my answer is wrong. Can somebody please guide me, what is the problem with it?? The question is:In 1999, Diana read 10 English books and 7 French books. In 2000, she read twice as many French...

Homework Statement I'm trying to show that the output of this XOR circuit is ##F=A'B+AB'##, Homework Equations ##(A+B)'=A'\cdot B'## ##(A\cdot B)'=A'+B'## The Attempt at a Solution From the gates the output is ##[(A\cdot B)+(A+B)']'##, using De Morgan's laws this becomes ##[(A\cdot...

I'll try to be concise. I've been out of math for years and never truly learned to understand it. Until now. I want to put the growth mindset theory to the test and see if I can handle physics (or any STEM field) on a university difficulty. To verify if I'm up to it and even have the slightest...

I am self teaching the subject but I am unsure of what is the whole point and picture