Combination Definition and 525 Threads

Given the vectors v1=(1, 1) ^t v2=(3, -1)^t setting up the matrix gives det≠0, thus any vector in R^n can be written as a linear combination of v1 and v2. This is where I'm getting confused. If the numbers in the matrix were changed so det=0, can you still right any vector in R^n as a...

In my textbook, The vector v is a linear combination of the vectors v1, v2, and v3 if there are scalars c1, c2, and c3, such that v=c1*v1+c2*v2+c3*v3. So c has to be a "scalar." To find these c values you can set up the augmented matrix (v1, v2, v3, v) and find the RREF. I'm a little...

var lost = [4, 8, 15, 16, 23, 42]; var count = lost.length; var isLost = function (n) { for (i=lost[0]; i<count; i=lost[i+1]) { if ( n === lost[i]) { return "true"; } } return "false"; }; is it possible to in corporate array positions into the for loop? (i) do...

Homework Statement Show that if c=\alpha{a}+\beta{b}, where a and b are arbitrary vectors and \alpha and \beta are arbitrary scalars, then c is coplanar with a and b. Homework Equations Triple scalar product: (a\cdot{b})\times{c}=0 The Attempt at a Solution...

Homework Statement Let S={r,u,d,x} be a set of vectors. If x=4r+4u+4d, determine whether or not the four vectors listed above are linearly independent or linearly dependent. If is dependent, find a non-trivial linear relation. Homework Equations The Attempt at a Solution I...

Question Source : Elements of Engineering Electromagnetics 6th edition by Rao. Page 202 problem3.30 Problem: Three sinusoidally time-varying polarized vector fields are given at a point by F1 = 3^(1/2) * ax * cos(wt +30) F2 = az * cos(wt+30) F3 = [ 0.5ax + 3^(1/2)ay + 0.5*3^(1/2)az ] *...

Homework Statement Compute the following: \int \frac{cosh(x)}{cosh^2(x) - 1}\,dx Homework Equations \int cosh(x)\,dx = sinh(x) + C The Attempt at a Solution I had no clue where to start, so I went to WolfRamAlpha, and it used substitution but it made u = tanh(\frac{x}{2})...

Homework Statement Several of us claimed that if d=gcd(a,b,c) then d is a linear combination of a,b and c, i.e. that d=sa+tb+uc for some integers s,t, and u. That is true, but we only proved the analogous claim for the greatest common divisor of two numbers, i.e. when d=gcd(a,b). We need...

My question is: For a vector x in a vector space V, is x a linear combination of itself? I'm not entirely sure since the definition of linear combination in the text I'm working through says: A vector x of a set V is a linear combination of vectors of S if there exists vectors in S such that x...

RESOLVED Homework Statement Let a = 123, b = 321. Compute d = gcd(a,b) and express d as an integer combination of ra + sb.Homework Equations This is a question (3.1, page 70 of Michael Artin's Algebra). For those who do not have the book, this problem is relevant to the section on subgroups...

Is there a way to define in how many ways can I form a number by it's portions? e.g: the number 5 has 6 ways: 1+1+1+1+1 2+1+1+1 2+3 2+2+1 3+1+1 4+1 I was trying to program that and would appreciate any help! Thanks.

So l am designing a radiation detector using solid state silicon photo multipliers. On their website they tell me that the SiPM must be coupled to a Cs(Ti) crystal with a combination of specular reflector diffuse reflector film between the scintillator and detector. How does a combination of a...

In how many ways can a committee of five be chosen from 11 people, if two particular people will not work on the same committee (that is, if one is included, the other must be excluded). I have attempted this questions with differents approaches and yielded the same answers, but my answer...

the given is 3mF is parallel to 11mF and 9mF in series connection and it is also parallel to 12mf and 6mf series connection my answer to this is 1.17*10^-5 is this correct

I'm writing a C++ program to brute-force solve a puzzle, but in order to determine the number of iterations the loop of the program should have (in order to exhaust all possible solutions) I need to know how many possible combinations there are. This isn't homework, I was just intrigued on how...

Homework Statement A toy rifle shoots a spring of mass 0.008kg and with a spring constant of 350 N/m. You wish to hit a target horizontally a distance of 15m away by pointing the rifle 45o above the horizontal. How far should you extend the spring in order to reach the target? Homework...

Homework Statement Show that linear combinations A-iB and A+iB are not hermitian if A and B (B≠0) are Hermitian operators Homework Equations Hermitian if: A*=A Hermitian if: < A l C l B > = < B l C l A > The Attempt at a Solution So I've seen this question everywhere but not...

This is, when it all comes around, just math. I am asked to prove that if the schroedinger equation looks like: \frac{d^{2}}{dx^{2}}ψ=-\frac{4πm}{h}*[E-U(x)]ψ(x) and ψ1 and ψ2 are two separate solutions for the same potential energy U(x), then Aψ1 + Bψ2 is also a solution of the equation...

Homework Statement Calculate the charge on C1 in Coulombs. Homework Equations umm q=CV The Attempt at a Solution http://answers.yahoo.com/question/index?qid=20120424171750AA1WxRv I have this same problem except my numbers are: C1= 6.00 μF, C2=3.10 μF, C3= 2.20 μF, C4= 1.30...

Homework Statement A class consists of 33 students 20 girls and 13 boys. Homework Equations We want to choose a team of 5 class representatives consisting of 3 girls and 2 boys. What is the possibility of choosing the 5 people. The Attempt at a Solution Using the...

Homework Statement The Attempt at a Solution I can't figure out how to do this problem. If you set the matrix up like this 2 -1 2 1 3 1 1 1 You can't solve it because there are 3 unknowns and two equations. I still don't really understand quite well when you set the...

I have been given this problem, I've simplified it down to a total resistance however I'm unsure on whether I have done it correctly. Any pointers would be nice, thanks. First of all I added the two resistors together in the top right as they are series. I then used that product with the...

How many different letter arrangement can be made from the 11 letters of MISSISSIPPI? (But using COMBINATION not the different permutation method) I saw an answer and it says: (combination of 1 out of 11)*(combination of 4 out of 10)*(combination of 4 out of 6) *(combination of 2 out of...

Question : Please give 8 weights which can weigh from 1 ... to 3280. you can put these 8 weights on either side of the balance, but you only can use once. Approach: have done few approach, most nearest one is 1,2,3,13,39,117,351,1053 but adds up to 1755 only,which mean i can only weigh...

Supposed to be A curious combo^ sorry Hello, I was just wondering what kind of prospects one might seek with a Environmental Biology and Mechanical engineering double major. I'm currently studying meche, but I love ecology and just typically being in nature. I've also considered this and...

Homework Statement How many way can a team lose 3 of their next 5 games? How many ways can a team lose 2 of their next 5 games? Why are the two answers the same? Homework Equations Permutation = nPr = n! / (n-r)! Combination = nCr = nPr / r! where, n, r are non...

Hi, My question is related to the following puzzle. “What is the highest number that can’t be created by adding any number of 4s and 9s”? For example, 25 can be created as follows: 9 + 4 + 4 + 4 + 4 =25 I know that the answer is 23. I also know that the general solution to such a...

Homework Statement Show that the eigenfunction of Lx can be written as a combination of eigenfunctions from Lz with the same l but different m. Using the eigenfunction Y_{x} = \frac{1}{\sqrt{2}}(Y^{-1}_{1} - Y^{1}_{1}) as the eigenfunction of Lx Homework Equations Y^{m}_{l} =...

Homework Statement I want to calculate the variance of a linear combination (b1, b2, b3, b4, b5, b6). I know what the variance equation is but I'm not sure if I have expanded it right. Homework Equations http://en.wikipedia.org/wiki/Variance The Attempt at a Solution Var(b1, b2, b3, b4...

combination problem: A football team consists of 3 players who play in a defence... Homework Statement http://www.xtremepapers.com/CIE/International%20A%20And%20AS%20Level/9709%20-%20Mathematics/9709_s05_qp_6.pdf 7 a ii (if exactly one forward player must be included, together with any...

Homework Statement Let Pn denotes the no. of ways of selecting 3 people out of 'n' sitting in a row if no two of them are consecutive and Qn is the corresponding figure when they are in circle . If Pn - Qn = 6 , then 'n' is equal to: The Attempt at a Solution Pn = (n-2) C 3 Qn =...

Homework Statement I know what's happening with the problem, but I just hate myself drawing all possible arrangements, I think I am too stupid, I hope better solution. Problems: 6 different Cookery books and 8 different History books are put on bookshelf. How many possible arrangements...

Hi, I have a problem that is giving me a headache. I have measured two angles that I believe to be related to one another, and they are (this is a data set where I have measured the angle from a datum to two features on a bone. There are 14 bones in the data set): Angles to feature 1 (F1)...

b]1. Homework Statement [/b] Find the total resistance of this complex combination of resistors. [ Homework Equations R(total)= (Rr)/(R+r) The Attempt at a Solution resistance of r(2) and r(3) = 20Ω resistance of the combination of r(1) and the resultant 20 Ω(ie r(2) and r(3) )...

Homework Statement The problem is about a rod that is set in a pendulum way but that has an angle high enough so the SHM doesn't apply to it. It starts at Pi/2 until it reachs 0. I was able to find the tangential and radial acceleration about the center of mass but now I need to know the x...

Homework Statement A 930 kg sports car collides into the rear end of a 2300 kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.9 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and...

Homework Statement Hello, it is a permutation / combination approach question, however, having thought about an hour i can't get any idea how it should be solved. Question is A coin is flipped n times, where n>=3 Find the number of ways to obtain (i) exactly two heads (ii) at...

Homework Statement For the circuit shown in the figure below, calculate the current I4 through the 1.94Ω resistor. As shown, R1 = 4.05Ω, R2 = 8.11Ω, R3 = 6.17Ω, R4 = 1.94Ω, I1 = 2.97A and E1 = 12V Homework Equations V=IR ƩI in a junction = ƩI out of a junction ƩV in a loop = 0 The...

Homework Statement In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together? (This is a question with solution I find on web, but I don't understand the solution) Homework Equations The Attempt at a Solution The...

Homework Statement I forget the exact expression of the questions. But the related details are exhaustive here. it's about permutation and combination. By the way, I am not student, i am looking for explanation and understanding, not answers.. 1. There are 6 people, namely A, B, C, D, E...

Homework Statement A circuit is constructed with five capacitors and a battery as shown. The values for the capacitors are: C1 = C5 = 4.6 μF, C2 = 1.7 μF, C3 = 5.7 μF, and C4 = 2.7 μF. The battery voltage is V = 12 V. 3) What is Q5, the charge on capacitor C5?Homework Equations Parallel...

Homework Statement Prove: Every nxn matrix can be written as a linear combination of matrices in GL(n,F). Homework Equations GL(n,F) = the set of all nxn invertible matrices over the field F together with the operation of matrix multiplication. The Attempt at a Solution I know all...

Homework Statement Given vectors {\bf r}=\left[r_1,r_2,r_3\ldots{}r_n\right]^T {\bf e}=\left[e_1,e_2,e_3\ldots{}e_n\right]^T I need to write the sum \sum_{i=1}^{n}r_ie_i^2 in terms of {\bf r} and {\bf e} Homework Equations Nil. The Attempt at a Solution Without...

So this was an exam question that our professor handed out ( In class. I didn't get the question right) Let E be a subset of R^n, n>= 2. Suppose that E measurable and m(E)>0. Prove that: E+E = {x+y: x in E, y in E } contains an open ball. (The text Zygmund that we used showed an...

Hi, I’m looking for a way to combine two discrete random variables (which I have as probability distributions). The combination should be the product (or other operation) of the two variables. This would be easy if they were independent, but they’re not. There is a known correlation between...

there are n students in a class. They are selected in sets of m. A student says he is selected a times. find value of a in terms of m and n. Total number of selections made are nCm. After that nothing is striking in my mind.can you please help.

Homework Statement A small wooden block, of mass M, lies in the middle of a horizontal table of length L and height h above the floor. The coefficient of kinetic friction between this block and the surface of the table is μ. A bullet, of mass m, is shot with a horizontal velocity into...

Hi, I have to solve a numerical problem namely how air is flowing first through a porous medium followed by streaming of the air coming out of the porous medium in a very narrow channel flowing to the ambient (journal porous air bearing). This problem can be described with the use of two...

Question is attached I have spent a great deal of time on this problem and I am hoping someone can help me out. My attempt at problem. first for the heat engine QL/Qw1 = TL/Twaste so efficiency = 1- Tl/Twaste efficiency = 0.93808 and I know that efficiency = Wout/ Qw1 This is as...

Homework Statement (1) Is the following formula right? \sum_{l=0}^{m+n} \sum_{k=l-m}^{n} \binom nk \binom {m}{l-k} x^{l} = \sum_{k=0}^{n} \binom nk x^{k} \sum_{j=0}^{m} \binom mj x^{j} (2) If right, how do I prove it? If not, what is the right formula, and how do I prove it? (3) Could...