Multiplication Definition and 484 Threads

Hello everyone I have trouble understanding the idea of multiplying two negative numbers. Why is product of such multiplication a positive number? Its so confusing.

Homework Statement Prove \sqrt{\frac{2}{\pi}}\int^{\infty}_0x^{-\frac{1}{2}}\cos (xt)dx=t^{-\frac{1}{2}} and use that to solve \int^{\infty}_0\cos y^2dy Is this good way to try to prove? Homework Equations The Attempt at a Solution Homework Statement...

Homework Statement I am given the group (G,\bullet) consisting of all elements that are invertible in the ring Z/20Z. I am to find the direct product of cyclic groups, which this group G is supposedly isomorphic to. I am also to describe the isomorphism. Homework Equations The...

This book says that if W^aX_a=0 and X_a is arbitrary, then I should be able to prove that W^a=0. I don't see how this is possible. This is the equivalent of the vector dot product, so if, say, X_a=(1,0,0,0), then W^a could be (0,1,1,1), and the dot product would be 1*0+0*1+0*1+0*1=0. Why would...

Homework Statement Hi, my question is whether the sum and multiplication of two periodic functions (with a common period) are periodic. Our functions are R\rightarrowR. Homework Equations The Attempt at a Solution f(x)=f(x+T) g(x)=g(x+T) T is the period. h(x)=f(x)+g(x)...

Homework Statement I'm having and issue with this problem, and I don't understand what I'm doing wrong, I really want to understand the material Write code that will print a multiplication table for 10 positive integers across the columns and 10 positive integers down the rows. Prompt the...

Homework Statement H is a nxn matrix with elements in {0,1} G is a nxn matrix with elements in GF(2) m is a nx1 vector with elements in GF(2). How can we perceive the output of HGm where Gm multiplication is in GF(2) and H multiplication is a normal real multiplication. Actually I want...

Homework Statement The Attempt at a Solution The above is my work. The problem is trying to make sure the inverse is element of the subgroup. Any leads? Also, was I correct in solving for x and y in that fashion?

Actually I have two questions Homework Statement Vectors A and B are shown on the figure below. Which one of the following statements is correct? a) A . B = 0 and A × B ≠ 0 b) A . B ≠ 0 and A × B = 0 c) A . B ≠ 0 and A × B ≠ 0 d) A . B = 0 and A × B = 0 Picture: http://i.imgur.com/X0GB9.png...

I need to show that addition and multiplication are well-defined in Z/nZ. So far, I've figured out that I need to work within this framework: Suppose a ~ a' and b ~ b'. Try to prove a + b ~ a' + b'. If a ~ a'...something If b ~ b'...something Any ideas?

Homework Statement A = { 1, 1, 2, 5} B = [1, 2] find A x B Homework Equations not much The Attempt at a Solution well, the problem itself seems easy enough The thing is, I'm not very sure what it means to multiply a set by an interval... just need a little help with this...

Homework Statement We are looking for the matrix A Homework Equations (A^transpose)^transpose=A The Attempt at a Solution i would start with finding the transpose of the matrix. -5 0 -8 -7

Homework Statement Let T:ℝ^{2}→ℝ be defined by T\left(\begin{array}{c} x_{1} \\x_{2}\end{array}\right) = (0 if x_{2} = 0. \frac{x^{3}_{1}}{x^{2}_{2}} otherwise.) Show that T preserves scalar multiplication, i.e T(λx) = λT(x) for all λ \in ℝ and all x \in ℝ^{2} The Attempt at a Solution...

A is an M × N matrix, B is N × K and C is a K × L matrix. Consider matrix multiplication (AB)ij = Pk AikBkj . Using the formula, (AB)ij = Pk AikBkj, how would I calculate ((AB)C) and (A(BC))?

This is similar to the question However, it is slightly different. It's probably more of a philosophy of math topic, however, I posted this on a philosophy forum and can't find many people interested in math there. I hope it hasn't been overly discussed. Thank you for reading even if you don't...

I've been googling but I haven't found anything useful. I am trying to understand how multiplying a matrix (or object of numbers - whatever you want to call it, like a matrix is 2D, a vector is 1D) of several dimensions works? I am writing some models for solving linear programs and it has a lot...

Okay, so before when I asked a question about voltage multiplication, I was recommended a charge pump. But now I realize that creating a charge pump to get the voltage I want would be rather ridiculous. So, here is my problem: I need to get 1000vdc from a 9vdc battery, but I'm not entirely...

Homework Statement d1 = 4i - 2j + 4k d2 = -5i + 5j - k Find (d1 + d2) * (d1 x 3d2) Homework Equations The Attempt at a Solution My first step was to add d1 and d2, which results in -i + 3j + 3k I then multiplied d2 by 3 to get -15i + 15j - 3k My problem is...

Hi, I am trying to find out what would be the significance of the result of multiplication of two marginal densities that originate from the integration of the a joint density function that connects them. To be more specific let's say we have a joint density function of two random variables...

Homework Statement Let U(n) be the set of all positive integers less than n and relatively prime to n. Prove that U(n) is agroup under multiplication modulo n Homework Equations The Attempt at a Solution n | a-a' implies n | b(a-a') =ab-a'b and n |b-b' implies n |a'(b-b')...

What is division? 12 ones split up into 3 things is 4 ones (per thing.) 1 one split up into 100 things is 1/100 ones (per 1 thing.) Thus, "5 ones split up into 1/100 things is 500 ones (per 1 thing)" is probably better understood as "5 ones split up among hundredths of a thing is 500 hundredths...

Homework Statement f(x)= 1/(5x2 +3) g(x)=1/(x-2)1/2 find (f+g)(x)The Attempt at a Solution for (f+g)(x) I use the common denominator by multiplying each side by (x-2)1/2/(x-2)1/2 and (5x2 +3/5x2 +3) respectively. I end up with a whole mess that I am unable to rearrange into anything useful...

Dear Forum, I have one question on matrix multiplication. Suppose there are 2 matrices - A = 1 -1 0 0 2 -1 2 0 -1 B = 1 1 2 and AB = 0 (Zero Matrix) if B not a zero-matrix, then rank(A) is less than s, where s is the dimension of B. I wanted to...

Hello, If I have block matrices A,B,C and D all of which are non singular would this relationship hold; my main concern is preserving order of matrix multiplication: if ADB=C then AD=B^-1C D=B^-1CA^-1 D^-1 = (BC^-1A) Also is it okay to assume the inverse of a block...

Homework Statement a) 50 b) 23 Product of the hexadecimal unsigned 8-bit integers Homework Equations Step Action |||||||||| Multiplicand ||||||| Product/Multiplier 0 Initial Vals ||||||||| 101 000 ||||||| 000 000 010 011 The Attempt at a Solution How...

Mutiplication of a scalar by a 0 gives 0(scalar) And also one proves in linear vector spaces that a vector(|>) combined with 0 by multiplicative law gives |0> . Similarly can one prove that multiplication of a tensor of say rank 2,by 0 will produce a null rank 2 tensor.

Hello, I'm wondering if there's some nice formula for the expansion of trinomials, like this: \prod_i \left(y + x - a_i\right) or for this: \prod_i \left(x^2 + a_ix - b_i\right) I know for instance that in the case of binomials there is the elementary symmetric polynomials available; thus...

I have a small problem where I remember I learned it in the past. But now I can't seem to recall how to do it. I searched on google, but I think even though it is probably really easy, I may not have worded it right to get the references I want. So I decided to ask here. Here is the problem...

I have read from my algebra book that the product of two complex numbers is still a complex number: (a+bi)(c+di)= (ac-db)+(bc +ad)i I was thinking that since complex numbers can be used to represent vectors, the product of two vectors should still be a vector. But I have also read from my...

If i have the mgf of X and the mgf of Y where X~N(mx,vx) and Y~N(my,vy) and X and Y are independent , then if i want to show that aX +bY ~ N(amx+bmy , a^2vx+b^2vy) how would i do this - need to be able to do the convolutions way and the mgf's way, for the mgfs way is it just, mgf(ax+by) =...

Hello, I am trying to write a program that multiplies together two 3x3 matrices. However my program does not really work as intended, and i get some really strange results. Any ideas? #include <stdio.h> #include <stdlib.h> int main() { int result_matrix[3][3]; int matrixA[3][3] = {...

I don't know how to construct formal proofs but there is the obvious geometric approach for 2 and 3 factors. However, how do you prove the commutative property holds up for 4+ factors? You end up with a lot of different orders in which you can multiply the factors and you can't just construct a...

Homework Statement If the series \sum_{n=1}^{\infty}x_n converges absolutely, and the sequence (y_n)_n is bounded, then the series \sum_{n=1}^{\infty}x_ny_n converges.Homework Equations Definitions and theorems relating to series and convergence.The Attempt at a Solution If the sequence y_n is...

I am wondering about ambiguous use of maths. Is there a clear answer? When you use parenthesis incorrectly the answer can come very unclear. For Example: A / B(C) Is quite ambiguous. Do you do the division first, or do you do the multiplication because of the juxtaposition. I...

I have a scalar function and a vector function and I need to make a scalar function as so: k=[kx ky kz] T=T(x,y,z) Function I want: div(k ? gradT) where "?" would be some operator that multiplies each component of k and gradT to make the vector [kx ∂T/dx , ky ∂T/∂y , kz ∂T/∂z] that way I...

I have read of dot product and cross product to multiply vectors, yet i do not understand the theory behind them. What are vector products even used for? Thank you.

Recently there was that long and ridiculous thread about ambiguity in notation when writing an expression. In the course of that discussion, someone posted a link from purplemath, which claimed that multiplication by juxtaposition was "stronger" than "regular" multiplication. However, this seems...

The class I'm in is not modern algebra nor have I take those courses. The professor of the class [Learning how to read/write in math] decided to try to teach some abstract algebra. I am trying to understand how multiplication is done in a field. I am using this site to help me as it was most...

Hello Is there any known operation/notation to express the multiplication of the entries of a rotated vector? More precisely, is there an alternative expression to replace the product operator for the following expression: \prod_i^3(RP)_i where R is the rotation matrix and P a vector in...

Hi All, I recently came across the interesting notion of constructing the minimal set of nxn matrices that can be used as a basis to generate all nxn matrices given that matrix multiplication, and addition and multiplication by scalar are allowed. Is there a way to construct an explicit set...

Homework Statement Prove or disprove and salvage if possible: for [a], [b] ∈ Zn for a positive integer n, if [a]·[b]=[0], then either [a]=[0] or [b]=[0]. The Attempt at a Solution I've managed to disprove the statement: Let n=6,[a]=3,and[b]=[4]. The[a]·[b]=[ab]=[3·4]=[12]...

A TECHNIQUE FOR MENTAL MULTIPLICATION (ALSO USEFUL FOR COMPUTER ARITHMETIC) When I was in Grade School, I was taught the standard way of multiplying numbers with more than one digit. I will describe the method only briefly, since it’s probable that everyone reading this will have seen and...

lets assume matrix A = [a]mxn and B = [b]nxp (AB)_{ij}=\sum_{r=1}^{n}A_{ir}B_{rj} why is that ? i guessed it would be (AB)_{ij}=\sum_{r=1}^{n}A_{ir}B_{jr} where m=p. so is there any logic behind that or its just random ?

I just read an article (http://www.maa.org/devlin/devlin_06_08.html ) saying that multiplication is not repeated addition. I am a first year engineering student, and i am very interested in mathematics. The picture i have had of multiplication for ~12 years or something is definitely of...

is multiplication of determinant commutative ? if so , then is this correct: |A||B|=|B||A|=|AB|=|BA| ? then what does |AB|=|BA| imply ??

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)...

Homework Statement Explicitly show, using numbers, that in general NxN matrix multiplication is not commutative. Show this for all N > 1. If I make a matrix A, 2x2, 1 2 3 4 and multiply by matrix B, also 2x2 5 6 7 8 I get AB =/=BA If I multiply a new matrix A, 3x3, 1...

Homework Statement hey guys... i try to do multiplication of two's complement number. I'm using straightforward method, which give me wrong answer.. i know i can't use this method.. but.. i just want to know why.. why i can't use this method? The Attempt at a Solution 1001 x 0101 = 0101101...

Why do we use significant figures in calculations instead of the rate of Uncertainty? (2,5\pm0,4000)*4,000=(10\pm1,6). The number 2,5 has 2 significant figures, which is the same as we will write in the answer, while it should be only one significant figure in the answer if we take the rate of...

I was surprised that I have never had to do this in so long and forgot the basic way to factor out a scalar multiple when a matrix is raised to a certain power (for example -1 for inverse matrices). Basically, I just want some confirmation: (λT)^n= λ^n (T^n ) ∶ for λ ϵ F and Tϵ L(V)...