Operations Definition and 317 Threads

Can I get this matrix \begin{smallmatrix} 1&1&0\\ 0&0&1\\ 0&0&0 \end{smallmatrix} from the identidy matrix I3 like this: \begin{smallmatrix} 1&0&0\\ 0&1&0\\ 0&0&1 \end{smallmatrix} Add second row to first row. Then substract second row from itself. Is the substraction of a row from...

This is a very basic question that I've been too embarassed to ask my elementary linear algebra teacher this far into the course: Lets say we have a matrix \begin{pmatrix} 1 & 2 \\ 2 & 1 \\ \end{pmatrix} Why can't we do something like ##R_2 - 2R_1## and ##R_1 - \frac {1}{2} R_2## at the...

First of all I must make a claim. Rules are shortcuts. Shortcuts that people use to not bother in understanding the complete picture of something. And this includes the rules of calculation between negative and positive numbers. Furthermore, I believe that these rules are counterintuitive or...

Is correct to state that: ##x \infty = \text{sgn}(x) \infty## ##\infty^x = \infty^{\text{sgn}(x)}## ?

Are set operations on a set ##X## defined as operations on ##2^X##? In other words a binary operation on ##X## is an operation ##\omega:2^X\times{}2^X\rightarrow{}2^x##? Surely the basic set operations could be defined that way, but then some weird non-standard operation like...

The Order of Operations: PEMDAS “A common technique for remembering the order of operations is the abbreviation "PEMDAS", which is turned into the phrase "Please Excuse My Dear Aunt Sally". It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction". This...

While working on an integration problem I found that I will arrive at two different solutions depending on how I approach it. I'm finding the arc length of y=ln(1-x2) on the interval [0,0.5] The formula for finding the arc length is ∫sqrt[1+[f'(x)]2]dx So f'(x) = -2x / ( 1-x2 ) Here...

Homework Statement I haven't been assigned these questions, but I'm trying to trudge through them to better understand symmetry. This is for my inorganic class. It's just a series of short questions like: C3 – S56 = ? S4 + i = ? C3 + i = ? Stuff like this. And just looking at the...

Hi, I am wondering why the order of operations where made? Is it the case that mathematics is just a tool of solving physical problems, and hence the order is physically defined? For example, if I say: I took 3 apples from 9 apples and divided the rest to two persons equally, I won't write...

1. So firstly I would like to show that product of the matrices L21,L31,... in the derivation of the LU decmoposition is lower triangular. I have already shown that product of upper and lower triandular matices is upper or lower. Now I don't know how to show the derivation. 2. I have been given...

Hello I have -csc^2 x Is this the same as -(cscx)^2 or (-csc x)^2? Thanks, Tim

Homework Statement If * is a binary operation on a set B, and the domain of definition is B^2, if * is associative and the neutral element is p. If r and l are elements of b we can say that r is a left inverse of l under * iff r * l = p, and l is a right inverse of r iff l * r = p. Show that if...

Python (numpy) question: I have two 2D numpy arrays, A[i,j] and B[k,l], but the indexes are unrelated to each other (A and B won't even have the same dimensions in general). I want to be able to add/multiply these two together to get a 4D matrix: C[i,j,k,l] = A[i,j] + B[k,l] or C[i,j,k,l] =...

Hi guys! I'm kind of stuck in my review here in Quantitave on the Polynomial part :confused: Homework Statement A. The first problem I had is Problem 7 on the link I will provide which has this. (x + y)3 + (x-y)3 = ? B. The second problem I had is Problem 8 on the same link I will...

Hey all, I have a four part question: Homework Statement Let ψ represent a wave function where x,y,z are spatial coordinates and t is time. The particles \pi^{-}, \pi^{0}, \pi^{+} are pions (\pi mesons). The parity inversion operation is represented by The Attempt at a Solution...

Hey all, I have a four part question: Homework Statement Let ψ represent a wave function where x,y,z are spatial coordinates and t is time. The particles \pi^{-}, \pi^{0}, \pi^{+} are pions (\pi mesons). The parity inversion operation is represented by The Attempt at a Solution...

I'm having trouble wrapping my head around what should be a trivial detail, but it is important, so hopefully someone else putting it in explicit words might help me understand it. What I am having trouble grasping is why do row operations preserve linear dependence relations for the columns...

Homework Statement Prove that replacing one equation in a system of linear equations by a non-zero multiple of itself does not change the solution of the system. The Attempt at a Solution I'm still relatively new to proofs, so this is what I have come up with: Let S be a system of...

Hey! Is it true that when you dot the del-operator on another vector, the differentiation has priority over the dot-product? That's why you get all those weird formulas for the divergence in circular and cylindrical coordinates (which are very different to the Cartesian ones)? So in the case of...

1. This problem examines the motion of an automobile traveling on a crest vertical curve with the following profile: y=100+0.1x-0.0005x^2 where y and x represent the roadway elevation (in feet) and the horizontal distance (in feet). The automobile sets the brakes when x=0 while traveling 45 mph...

I know that the example I use has been done online many times, but my question isn't about how to get the answer, that is obvious, my question goes a little deeper. For example when deriving the equation for an ellipse we have the constraint that the ellipse equation describe the set of (x,y)...

How do these operations with Del operator work?? Homework Statement Let's say A and B are expressed by their cartesian components as: A = <P, Q, R> and B = <M, N, O> what would be the differente between (A.∇)B and B(∇.A) ? Homework Equations The Attempt at a Solution I tried...

I was wondering if anyone would be able to help me in answering these two questions related to this problem. I'm rather stuck! Problem - Ronald has just discovered four new ingredients for making a very potent potion that will raise his IQ by 15 points. We can only identify the ingredients as...

just want to know if my answers are correct. 1. for any set A, a set of subsets of A is said to be exhaustive if the union of these subsets is A, and is said to be disjoint if no two of the subsets have any element in common. if $\displaystyle A\,=\,\{a,\,b,\,\,c\},\,$ tell whether the...

just want to make sure if my answer is correct If $\displaystyle U\,=\,\{0,\,1,\,2,\,3,\,4,\,5,\,6,\,7,\,8,\,9\}$, the set of digits in our decimal system, and $\displaystyle A\,=\,\{0,\,1,\,2,\,3,\,4,\,5\}$, $\displaystyle B\,=\,\{2,\,3,\,4,\,5,\}$, $\displaystyle C\,=\,\{4,\,5,\,6,\,7\}$...

please help me understand what my book says: If set A has only one element a, then $\displaystyle A\,x\,B\,=\, \{\left(a,\, b\right)\,|\,b\,\epsilon\,B\}$, then there is exactly one such element for each element from B. can you explain what it means and give some examples. thanks! :)

How does this formula SPI = EV / PV rearrange to this formula EV = SPI * PV Why does the operation change from multiply to divide? Thanks for the help.

Suppose we are given a binary operation on a finite set of abstract symbols in terms of a multiplication table such as: \begin{array}{c|ccc} * & A & B & C \\ \hline A & A & B & C \\ B & B & A & B \\ C & C & B & A \\ \end{array} Suppose we want to represent the operation in some...

If a, b and m > 0 are integers such that a % b (mod m), then a^n % b^n (mod m) for all positive integers n. I don't know how to go about it, any help would be greatly appreciated.

I'm trying to get my words right. They say you can't do operations on infinity. Sorry I don't have an exact quote. But on the other hand you can do calculations involving infinite series. What is the proper way to describe what math can't do with infinity? I want to say something along...

Consider the reduce operation for example. Do all nodes send data directly to the root? Or is there some structure where a node will receive data from a few other nodes, perform a reduction, then pass the intermediate results to other nodes?

I have gained a place on the graduate rotational leadership programme at a major heavy industrial company which involves me going to different divisions to lead projects. I have been given a choice of either going down the R&D path or the Operations Management path. Being an engineer from a top...

What allows you to add the same quantity to both sides of an equation? Is this an axiom? A property of addition by which addition is defined? Or both? What about for multiplication? If you differentiate both sides of an equation, the resulting equation will be valid, provided both sides of...

I'm trying to figure out how to multiply and add square (3 X 3) matrices with Perl (without PDL) in which each matrix is in a separate file, but I haven't been making any progress. I'm a Perl beginner, so does anyone have any suggestions for examples/resources that may help me? Thanks.

I use the ternary operation in web development all the time, eg: x = y > z ? a : b Which reads, if x > y then a, otherwise b I realize that it is just a shorthand for if...else statements, but even still, are there any mathematical properties associated with it? I know inequalities have...

1. Solve the matrix using elementary row operations 2. {3, 1, 4 1, 4, 3 4, 3, 1} 3. I keep trying to solve this, but I keep getting odd numbers, can someone help?

Homework Statement A lemming marches off an ice berg, falling directly downward from a height of 12.40 meters. 0.10 seconds later, he is 9.151 meters above the ocean below. 0.20 seconds this altitude is reduced to 5.804 meters, and at 0.30 seconds he as fallen to 2.359 meters above the...

I have a rather technical question in boolean algebra to which I was not able to find an answer. What is the order of operations in boolean algebra? Is it first logical NOT, logical AND, logical OR, and finally logical XOR? Correct me if I am wrong. BiP

This question is fairly simple: what is the difference between functions and operations. Both seem to have inputs and outputs. Both can input/output scalars, vectors, functions, functionals, etc. I think the sticking point might be mapping, but I'm not sure. E.g. f=a+b vs. f(x,y)=x+y

Homework Statement $$ \overrightarrow {F}=3xz^{2}i+2xyj-x^{2}k $$ $$\phi =3x^{2}-yz $$ are given vector and scalar fields, respectively. a) $$\quad \operatorname{div}\left( \operatorname{grad}\phi \operatorname{div}\overrightarrow {F}\right) =\quad? $$ b) $$\quad...

Homework Statement Given a limited set of operators, specifically increment and bitshift left (only 1 bit at a time) Calculate the number of operations required to get from a certain number to another. Eg. 9 to 20 = 2 [(9++)LSHIFT] Homework Equations The Attempt at a Solution I...

I'm playing around in Python at the moment, and I came across an exercise to perform bitwise operations manually (without the built in & | ^ ~ operators). I understand the operations on paper, and I have a function here that performs them (& in this case, the others are similar): def...

Sorry for disregarding the template; I'm not really working out a homework problem as much as just trying to follow the reasoning in the text. I'm working through the first chapter of Quantum Mechanics, McIntyre, and I'm a little bit confused by the following. The text introduces bra-ket...

Hello all. Just a quick question about logical operations gears can preform. I know if you have a large gear turn a small gear, the center of the small gear will spin faster than the large. But are there any other logic operations that gears can preform? Thank you for viewing.

Homework Statement Execute the arithmetic operations using 6-bit binary numbers in 2's complement representation. 18+11 (just going to list this first task) Homework Equations To convert from regular binary number, from LSB, do not invert initial o's, or first 1, but invert all other...

Hello, i would like to ask the following question that has been troubling me. lets say i have 1/3 = 0.33333333333(3) it may seem clear that 1/3 - 1/3 = 0, but when operating over the decimals this doesn't seem clear. How can i perform an operation over infinite digits and consider it as...

Sorry if the title of my question is wrong, lim sup_n A_n = ∩^∞ U^∞ A_k does it mean that first we are taking the union of A_n and then we are taking intersection? actually I am confused, what is it actually?

I apologize for the repost, but I had no replies to my previous post. I figured that I didn't put down a good enough attempt of a solution. I will try to explain what I did in more detail. I have read the rules for the forum, but if I'm still doing something wrong, please tell me. I want to...

Hello everyone! Is there a conventional notation for some common arithmetic operations, like element-wise product, or element-wise power? Thanks!

Is there a better/different way of indicating the order of operations in a mathematical expression - other than using parentheses?