Operations Definition and 305 Threads

if you perform row operations on a matrix A to convert it to the identity matrix and then use the same row operations and apply it to another matrix B, why is it that the end result of B^r does not depends on B's actual sequence

Suppose you are given (1) a natural number N; (2) a set of natural num- bers S = {n1; n2; : : : }; (3) a set of arithmetic operators, say +; -;*; = (with the usual meaning of addition, multiplication, substraction, di- vision). Your job is to construct an arithmetic expression R built from...

I realize now that I took something for granted when I first learned it god knows when.. So I though of starting a discussion as to why were the order of operations defined the way they were? I mean, is there some kind of natural explanation as to why we should compute exponents first and...

SplashDamage's question from Math Help Forum, Hi SplashDamage, There is no such thing as "moving" a term to the other side. A equal sign means that both quantities same quantitative amount. Therefore you can add, subtract, divide or multiply both sides of the equality by the same number and...

Like many math newbies, complex numbers (or at least the idea of complex numbers) are a source of some confusion... but I've worked with them before and I'm reading through posts on PF that I hope will give me some sense of intuition about them. That said, there is one nagging question that I've...

Hi, I need to generate some data in a Table and then be able to do all kinds of matrix and other mathematical operations on them. Right now I am testing the commands but am unable to get them to work. My table has this extra parenthesis floating around which I'm not sure how to get rid of...

question in attachment. please help!

Ok, so I am taking my first course in linear algebra, and even though I am not a math major (physics major actually), I can't help but wish my teacher and text were more rigorous. So let me start by telling you all the problem I am having: (First question) My book states the following...

Hi All, So here's my question: Suppose we have two sets A and B, then A \setminus B denotes their set-difference. Does there exist an equivalent operator for the case where A and B are not sets, but sequences? Otherwise, is there an operator to convert a sequence into a set...

Homework Statement Determine the values of k for which the system of linear equations has (i) a unique solution, (ii) no solution, (iii) infinitely many solutions. Write down the complete solution in cases (i) and (iii): x + y + kz = 1 x + ky + z = 1 kx + y + z = 1 Homework Equations...

i know you have the 3 row operations. add two rows. multiply a row by a constant. add a multiple of a row to another. my question is can you multiply a row by a constant to clear a fraction at any time so long as you end up in row echelon form. no matter what operations you do the result in...

I am writing some code which involves numerical integration of a function on a 3D grid of points. I am defining the type vector to refer to these points, and I am also trying to extend the intrinsic operator * to include scalar and vector multiplication. However, I cannot compile and I don't...

I'm working on the following two proofs: 1.) (x+y)2n+1 = x2n+1 + y2n+1 if and only if x=0, y=0 or y=-x and 2.) (x+y)2n = x2n + y2n if and only if x=0 or y=0 I've tried using induction and get stuck at a certain point. I've also tried playing around with...

Hello all. Currently working on simplifying some Boolean expressions, one of the questions is: ( A int B U C) int B I do not know how to go about simplifying the first term because there are not any parentheses within it and I have both the intersection and union symbols. Is there an...

Just wanted to clarify.. The operation of the Riemann Sum is addition. It can also be used to signify subtraction by adding negative numbers. We also have an iteration of multiplication by using exponents. For example, 2^3 = 2 * 2 * 2. But even then the complexity doesn't reach to that...

In first year, I learned that PAP-1 = D. Now, I am learning that S+AS = A(v). (where the + sign is a dagger) It seems like both of these operations diagonalizes the matrix A, but doesn't feel like they are the same thing, unless they are the same thing.

So, I'm trying to learn prolog, and since it's used a lot in the AI community, I thought I would try my hand at implementing a few of the simple "wumpus world" rules. The rule for a "pit" existing at location (2,2) means that a breeze is felt at locations (1,2), (2,1), (2,3), and (3,2). So...

Hello, I tried to figure out what is the maximum count of arithmetic operation (*,:,+,-) need for gauss elimination and gauss-jordan elimination, but can not get it right. what I get from wikipedia is but I don't understand how to get to this result. Thanks for any help.

Heres two problems from an A Level related paper: prove that if pq is irrational then atleast one of p or q is irrational. Also prove that if if p + q is irrational then atleast one of p or q is irrational. These two proofs are trivial proof by contradiction problems but it got me thinking more...

Homework Statement The 3x3 matrix A is transformed into I by the following elementary row operations R1+2R3 -> R1 R2+2R3 ->R2 2R2 ->R2 R1 <->R2 2R3 ->R3 Find det(A) Homework Equations I assumed to start off with the problem since I was going backwards from I to A. I would do the opposite of...

Homework Statement Consider the following 3 row operations performed to a 4x3 matrix A used to transform it into matrix B: E1: -4R1+R4-> R4 E2: R2<->R3 E3: (1/2)R4-> R4 From there I am asked to find E1, E2, E3. The Attempt at a Solution I assumed the identity matrix I would start...

I'm trying to find a set of five (5) algebraic functions a(x), b(x), c(x), d(x), and e(x) that for every order they can be applied, will produce a unique result. That is, a(b(c(d(e(x))))) should be different from e(d(c(b(a(x))))) for every possible x. And every other unique ordering should...

Do any such programs exist?

Let me explain further my question by what i mean 'operation'. An 'operation' can be on a single number, example sqrt(2). An 'operation' can be 'binary' between two numbers, example 1+2. An 'operation' can be performed on more than two elements, example placing vectors on a grid and finding...

Are you allowed to mix and match row and column operations? For (a), using only row operations, I cannot get the matrix into the form they want. Could I swap a few of the columns around to do so? For (b), I got it into the form they want. The rank of the matrix is 2 because I have I2 there...

Hello I am trying to teach myself how to use mathcad and am having some issues. I am trying to sum the rows and cols of a matrix respectively. using i for the row index and j for the col index. I have as of now defined a variable sum eiether row or colum and am using a summation of...

Hi all, I am not sure if this is the right place to ask but I have two problems which I require enlightenment. The questions are, 1) Show that the intersection of two lines can be computed by rational operations. 2) Show that the intersection of a line and a circle can be computed by...

I want to have broad opportunities after my degree, and with the new ideas floating in health care, Actuarial Science might seem like a career that may experience some downsizing. Now, I was also interested in Operations Research as well, and my university offers both in the math...

How are the tensors of General Relativity simplified and operated? And can someone give me a mathematical example of General Relativity being done with just some basic values being plugged in for G=kT?

I am unsure what is meant by binary operation. Is the binary operation of addition : addition and subtraction or is it just addition?

I am trying to the following operation * is closed under R (the real numbers). x * y = x + 2y + 4 Check commutability - NOT commutative x * y = x + 2y + 4 y * x = y + 2x + 4 Check associativity - NOT associative x * (y * z) = x * (y + 2z + 4) = x + 2(y + 2z + 4) + 4 = x + 2y + 4z +...

Hi guys, I'm having trouble solving the following questions. 1) Show that the line through two rational points has an equation with rational coefficients 2) show that a circle whose center is a rational point and whose radius is rational has an equation with rational coefficient. Cheers

Hi everyone, I am an industrial engineer who is on a internship. For the purposes of my work, I need to understand the major components and operations of electric generators; I am not looking for knowledge that would allow me to design and critique, but just seek sufficient knowledge that would...

Homework Statement okay. So here is the problem: x= 48÷2(9+3) Homework Equations The Attempt at a Solution So, what I am thinking, is how should the order of operation should be followed. There are different answers when tried using a different order of solving. So...

I've been studying Turbulence, and there's a lot of averaging of differential equations involved. The books I've seen remark offhandedly that differentiation and averaging commute for eg. < \frac{df}{dt} > = \frac{d<f>}{dt} Here < > is temporal averaging. If...

Hi everybody! I recently came across the hyperoperation sequence which extends the sequence of operations x+y, x*y, x^y to operations x[n]y, which are recursively defined as "the previous operation applied y times on x". So I asked myself: Can this be generalized to positive rational (or even...

Hi Again: Just curious: I know that, given a system of linear equations, ERO's (scaling both sides of an equation, exchanging/swapping rows and adding a multiple of a row to another row) preserve solutions, i.e., if x is a solution to Ax=b, then swapping rows will preserve x as a...

Hello Experts, I post this question here because in the homework topics there is no abstract algebra! Please help me I want to understand it: I have a ring R with unit. Also I am given n - natural number, I_n is the set {x in R: n*x = 0} I have to prove or refute: Given n, m natural...

Hi, Everyone: A question about finding the inverse of a matrix M using elementary row operations (ERO's) E_k (where E_k is either a row-exchange, a scaling of a row by k, or adding the multiple of one row to another row ) to do row-reduction in reduced-row-echelon format, to end...

Homework Statement An airplane is traveling with airspeed of 225 mph at a bearing of 205 degrees. A 60 mph is blowing with a bearing of 100 degrees. What is the resultant ground speed and direction of the plane? Homework Equations x = u cos(degrees) y = v sin(degrees) However, I think the...

Homework Statement I just started in calculus ii ,and I remember that most I didn't use specific rules when dealing with derivatives and I sometimes managed to get away with it(especially in physics. now I have been playing with relations and I got unacceptable results so i will post what I...

I've gotten claims that infinity is not a number but an idea. How do infinities work in operations? Are there "smaller" and "bigger" infinities? If ∞+1=∞, is ∞-∞=1?

Hello everyone! I am trying to construct an algorithm for the following problem and was wondering if there is any existing body of knowledge on this. Please forgive me if this is inappropriate (or ridiculous) but I am totally foreign to number theory. It goes like this: You are given n...

Homework Statement Determine whether the operation has an identity element. x*y = 3xy Homework Equations e*x = x*e = x, if this holds, e is an identity element The Attempt at a Solution My attempt: x*z = z*x = 3xz, then 3xz = x <=> z = 1/3 => e = 1/3. But the answer key in the...

Homework Statement then what are the operations that maintain the Inequality and what are the operations that don't? Homework Equations The Attempt at a Solution clearly addition and subtraction maintains it ,and so does multiplication and division by any number other than...

1) If A = [aij] is an n x n matrix, the trace of A, Tr(A), is defined as the sum of all elements on the main diagonal of A, Tr(A) = the sum of (aii) from i=1 to n. Show each of the following: a) Tr(cA) = cTr(A), where c is a real number b) Tr(A+B) = Tr(A) + Tr(B) c) Tr(A(Transpose)) = Tr(A)...

Hi I'm a layman so please keep your reply as simple as possible. Thanks. They say that a CPU has built-in circuitry to do simple arithmetic operations such as addition, subtraction, etc. and logical operation such as greater than, less than, etc. I don't understand how could some...

Just out of curiosity, would a class in operations research be worth the time for someone majoring in physics, hoping to go to graduate school for theoretical physics/cosmology?

Homework Statement Let R1 and R2 be the "congruent modulo 3" and "congruent modulo 4" relations on the set of integers. Homework Equations Find: a) R1 \cupR2 b)R1 \cap R2 There is also problem c, d but I won't write these here. If I am able to solve this, then the rest should be...

Homework Statement Find a sequence of continuous functions f_n: R \rightarrow R such that lim_{x \rightarrow 0}lim_{n \rightarrow \infty}f_n(x) and lim_{n \rightarrow \infty}lim_{x \rightarrow 0}f_n(x) exist and are unequal. Homework Equations N/A The Attempt at a Solution I...