Multiplication Definition and 496 Threads

Homework Statement Homework Equations Is my solution correct? If not then please point out the mistakes and help me solve this question in the right way. Thanks in advance. The Attempt at a Solution

I am exploring Gaussian integers in terms of roots, powers, primes, and composites. I understand that multiplying two integers with norm 5 result in an integer with norm 25. I get the impression that there are twelve unique integers with norm 25, and they come in two flavors: (1) Four of them...

I am trying to multiply hexadecimal numbers. Here is what my book has given Here is my solution book solution and my solution has differed in the red marked area. which solution is correct? am I doing anything wrong here? I get 6 F but book wrote 78 in that red marked area. Need...

The picture shows a simple problem. However, my question has to do with multiplication of radicals. I know how to use FOIL. sqrt{x - 3} • sqrt{x} is slightly confusing. Do I multiply radicand times radicand? My question is: Does sqrt{x - 3} • sqrt{x} become sqrt{x^2 - 3x} in the FOIL...

I have two functions ##\phi(t)=\cos(\omega t)## and ##f(t)=u(t)−u(t−k)## with ##f(t)=f(t+T)##, ##u(t)## is the unit step function. The problem is to find Laplace transform of ##\phi(t) \cdot f(t)##. I have tried convolution in frequency domain, but unable to solve it because of gamma functions...

My question is perhaps as much about the philosophy of math as it is about the specific tools of math: is perpendicularity and rotation integral and fundamental to the concept of multiplication - in all number spaces? As I understand it, the product of complex numbers x = (a, ib) and y = (c...

Let's just talk about unit quaternions. I know that $$\left(\cos{\frac{\theta}{2}}+v\sin{\frac{\theta}{2}}\right)\cdot p \cdot \left(\cos{\frac{\theta}{2}}-v\sin{\frac{\theta}{2}}\right)$$ where ##p## and ##v## are purely imaginary quaternions, gives another purely imaginary quaternion which...

Homework Statement So basically, I have to implement the algorithm given in the relevant equations section. Homework Equations The Attempt at a Solution First and foremost, my code. Some bits that weren't directly relevant to the problem I'm having were removed for readability's sake...

Hey, I have often times wondered what is multiplication? Repeated addition is OK but for some reason it doesn't satisfy me. For example: 2*2cm is linear because it scales 2cm on the same dimension but 2cm*3cm is not scaling, it spans 2 dimensions. It seems as if the flow of operation takes a 90...

I got my education out of the American continent, yet currently I live in Canada and my son goes to school here (5th grade + some additional math training) What puzzles me is that currently he may write things like $$5\times-1$$ meaning ##5\cdot(-1)##, which I can only read as ##5x-1## (i.e...

Homework Statement In my text, it had a quick side note on solving basic equations. It related to clearing decimals by multiplying by an appropriate factor of ten. For example, 0.25x + 0.10(x-3) = 1.10 can be cleared of decimals by multiplying the decimals by 100, which would result in 25x...

Homework Statement Homework Equations Matrix multiplication. The Attempt at a Solution Answer given=4 What am I doing wrong??

Suppose we have two vectors ##a = [1,2,3]## and ##b = [4,5]##. I want to construct the matrix of products, i.e. $$ \begin{bmatrix} 1\cdot 4 && 1\cdot 5\\ 2\cdot 4 && 2\cdot 5\\ 3\cdot 4 && 3\cdot 5 \end{bmatrix} = \begin{bmatrix} 4 && 5\\ 8 && 10\\ 12 && 15 \end{bmatrix} $$ Does anyone know an...

I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ... I am currently focused on Chapter 1: Construction of the Real Numbers ... I need help/clarification with an aspect of Theorem 1.2.7 (1) ... Theorem 1.2.7 reads as follows: https://www.physicsforums.com/attachments/6976...

As we know that 2×3 = 2+2+2 = 6; so similarly what does matrix multiplication represents?

Hi, to understand finally the Laue equation for diffraction I am missing something : h*p+k*q+l*r = integer. Given that p,q,r are integers how come h,k,l MUST BE INTEGERS as well? Say p=q=r=2, than h=k=l=1/2 works just fine. I understand that there is something about a common...

##\begin{align}[A(BC)]_{ij} &= \sum_r A_{ir}(BC)_{rj} \\ &= \sum_r A_{ir} \sum_s B_{rs}C_{sj}\\ &= \sum_r\sum_s A_{ir}B_{rs}C_{sj}\\ &= \sum_{s} (\sum_{r} A_{ir} B_{rs}) C_{sj} \\ &= [(AB) C]_{ij}\end{align}## How did it went from ##2## to ##3##. In general is there a proof that sums can be...

What is the physical meaning of multiplication when we multiply two quantities in physics to get a single quantity? Eg. Mass * acceleration = force.

I am finding it hard to understand this questions its sounds more like fraction subtraction than multiple but the army test sample questions says its multipication You have 3 1/4 boxes of paper. You give 1/2 to the paper to a colleague, how many boxes of paper do you have left. The test says 1...

What would be the easiest (but neat and readable) way of entering a 4 element by 4 element multiplication table ... ... for example the multiplication table for the field of 4 elements ... ... Peter

Why is the dot product equivalent to the matrix multiplication of its components? I've seen some proofs using Pythagorean and cosine law but they don't give you an intuitive feel as to why matrix multiplication works. The geometric definition (##ab cosθ##) is very easy to understand. To a...

In how many different ways can we arrange three letters A, B, and C? There are three candidates for the third position that leaves the two remaining letters for the second position and so 3 times 2 is 6 and One is the multiplicative identity I am astonished by The commutative property of...

I try to write volume calculation equation in latex using both multiplication and deltat which is producted with velocity and quarter square of diameter to calculate volume. Vvolume=Vvelocity$$\frac{diamter^2}{4}\deltat$$ Would you please explain what is wrong with the code? Thank you.

Hi, what does it mean to cross multiply two vectors? I couldn't imagine them in real life. eg Force vector. Multiplying Force vector to a scalar value means you multiple the 'Strength' of the force, Dot multiplication of Force with displacement to get work, means you get the work in...

Homework Statement Homework Equations RAO = b(Sinβj+Cosβk) The Attempt at a Solution [/B] The box in red is ω. However I am unsure of where they got the box in blue from? As mentioned above, RAO = b(Sinβj+Cosβk) so not sure where they got the box in blue from? I know of the vector triple...

Here's a fun way to do multiplication graphically that originated in Japan:

Hi, I am studying Matrix chain Multiplication to find out the optimal way of multiplying a series of matrices so that we can reduce the number of multiplications. I have got this example from the book which multiplies the matrices having dimensions given below: A1 30 * 35...

Homework Statement Show that the set GL(n, R) of invertible matrices forms a group under matrix multiplication. Show the same for the orthogonal group O(n, R) and the special orthogonal group SO(n, R). Homework EquationsThe Attempt at a Solution So I know the properties that define a group are...

Homework Statement "ℝ×ℝ and ℂ are very similar in many ways. How do you realize ℂ as a Cartesian product of two sets? Consider how complex numbers are multiplied; by grouping real and imaginary parts, show how the pattern of complex multiplication can be used to define multiplication in ℝ×ℝ...

Hey! :o Based on the definition of $+_k$, I want to give an inductive definition for the multiplication $\cdot_k$ in $\mathbb{Z}_k$, such that for all $x\in \mathbb{N}_0$ and $y\in \mathbb{N}_0$ it holds that $$x\cdot_k y=(x\cdot y)\mod k$$ What is an inductive definition? (Wondering) Do...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with the proof of Lemma 1.25 ... Lemma 1.25 reads as follows: My questions on the proof of Lemma 1.25...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with the proof of Lemma 1.25 ... Lemma 1.25 reads as follows: My questions on the proof of Lemma 1.25 are as...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need some further help with the statement and proof of Lemma 1.24 ... Lemma 1.24 reads as follows: My further...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need some further help with the statement and proof of Lemma 1.24 ... Lemma 1.24 reads as follows: My further questions regarding...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with the proof of Lemma 1.24 ... Lemma 1.24 reads as follows: My questions regarding the proof of Lemma...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with the proof of Lemma 1.24 ... Lemma 1.24 reads as follows: My questions regarding the proof of Lemma 1.24 are as...

I was reading Armstrong's Groups and Symmetry the other day and saw this table. It has beautiful symmetry. It is the the prime numbers multiplied modulo 8. It creates one of the most elegant things I've ever seen. What is so special about modulo 8 that creates such a symmetric matrix of primes?

How can one define addition using peanos axioms? Number, successor, zero are terms which we presume to know the meaning of. We then use five propositions: 1. 0 is a number. 2. Every number has a successor. 3. 0 is not the successor of any number. 4. Any proeprty common to zero and its...

The only thing which makes complex numbers different from 2-dimensional vectors or any other two-component mathematical object is their multiplication, right? Complex multiplication has uses in rotations but we can easily achieve that using polar co-ordinates. And, their other applications in...

It seems like division between two units is a simple intuitive concept to grasp, such as velocity, for every interval of time, a particle travels a certain distance. However, I've always had trouble trying to find an intuitive sense for multiplication between two units, e.g. what exactly does...

This problem is a little elementary, If we were to multiply the fraction $\frac{3}{7}$ by two which way should I be using, $2\left(\frac{3}{7}\right)=\frac{6}{14}$ --------------- 1 or $\frac{2}{2}\left(\frac{3}{7}\right)=\frac{6}{14}$ --------------- 2 I usually multiply fractions using...

Hello everyone. I wanted to prove the following theorem, using the axioms of Peano. Let ##a,b,c \in \mathbb{N}##. If ##ac = bc##, then ##a = b##. I thought, this was a pretty straightforward proof, but I think I might be doing something wrong. Proof: Let ##G := \{c \in \mathbb{N}|## if ##a,b...

Suppose that I have an overdetermined equation system in matrix form: Ax = b Where x and b are column vectors, and A has the same number of rows as b, and x has less rows than both. The least-squares method could be used here to obtain the best possible approximative solution. Let's call this...

The problem Consider field ##(F, +, \cdot), \ F = \{ 0,1,2,3 \}## With the addition table: Find a multiplication table. The attempt Please read the most of my answer before writing a reply. My solution was $$ \begin{array}{|c|c|c|} \hline \cdot & 0 & 1 & 2 & 3 \\\hline 0 & 0 & 0 & 0 & 0...

Great question. In algebra, we do indeed avoid using the multiplication sign. We'll explain it for you here. Watch the next lesson: https://www.khanacademy.o...

Software for multiplication of matrices I'm going to do a lot of matrix multiplications, since I'm computing Jarlskog invariants. I would like to know if there is a great program for doing a lot of matrix multiplications? I tried with Maple but at some point it gives up. My matrices are not...

$\displaystyle \begin{align*} A\,A^T &= \left[\begin{matrix} 3 & 0 & -4 \\ 4 & 0 & \phantom{-}3 \\ 0 & 5 & \phantom{-}0 \end{matrix}\right]\left[ \begin{matrix} \phantom{-}3 & 4 & 0 \\ \phantom{-}0 & 0 & 5 \\ -4 & 3 & 0 \end{matrix}\right] \\ &= \left[ \begin{matrix} 3\cdot 3 + 0 \cdot 0 +...

This is I think a really dumb question, but I never got it, why do we have that dot symbol when we integrate. Like in gauss's law, we have ∫E⋅dA . why is that ⋅ there? Thank you for your help

Let A = (a_{ij}) be a k\times n matrix of rank k . The k row vectors, a_i are linearly independent and span a k-dimensional plane in \mathbb{R}^n . In "Geometry, Topology, and Physics" (Ex 5.5 about the Grassmann manifold), the author states that for a matrix g\in...

Hey guys, I really need help in revising my Axiom 6 for my Linear Algebra course. My professor said, "You need to refine your statement. You want to show rx1 and rx2 are real numbers. You should not state they are real numbers." Here is my work: Proof of Axiom 6: rX is in R2 for X in R2...