System of equations Definition and 285 Threads

Hi, In a project of mine I've encountered the following set of equations: $$ \sum_{i=1}^N \left(\frac{1}{M}\sum_{\alpha=1}^Mg_{ij}^\alpha - u_{ij}^* \right) = 0 \qquad \forall: 1\leq j \leq N$$ $$\sum_{i<j}\left( (u_{ij}^*)^2 - \frac{2}{M^2}\sum_{\alpha < \beta}^Mg_{ij}^\alpha g_{ij}^\beta...

I have 2 ellipsoids: Ax^2/a^2+Ay^2/b^2+Az^2/c^2=1; (*a,b,c>0 constants*) Bx^2/a^2+By^2/b^2+Bz^2/c^2=1; Ellipsoid A rotates around axis [wax;way;waz] (unit vector) with an infinite speed; Ellipsoid B rotates around axis [wbx;wby;wbz] (unit vector) with an infinite speed; [Dx;Dy;Dz] is the vector...

I am solving the following system of equations (in matrix form): ##\begin{pmatrix} 1 & -2 & -1 & 1 \\ 2 & -3 & 1 & 6 \\ 3 & -5 & 0 & 7 \\ 1 & 0 & 5 & 9 \end{pmatrix}## I want to solve it using Mathematica, but when I use the command LinearSolve[], I only get back ##\begin{pmatrix} 9 \\ 4 \\ 0...

This is actually not a homework problem, but a problem I'm encountering while working on a little project and I'm not sure if it's even solvable or if it makes sense what I'm doing 1. Homework Statement First, I have the equation $$p_{ij} = \frac{1}{2}\left( \tanh{(-\frac{\theta_i +...

Hey! :o A national economy has $3$ sectors: fishing, forestry, boat building. One fishing boat is needed, to catch two tonnes of fish. To produce four tonnes of wood, one tonne of fish is needed to feed the forestry workers. Two tonnes of wood are needed, to build one fishing boat. There...

Homework Statement Let ##n## be some natural number. Solve the following ##n \times n## homogeneous system of equations: $$\sum_{1|i} x_i = 0$$ $$\sum_{2|i} x_i = 0$$ $$\vdots$$ $$\sum_{n|i} x_i = 0$$, where ##a|b## means ##b## is divisible by ##a##. Homework EquationsThe Attempt at a...

Hi, Is it possible to solve such an equation used as a must at my job? 1- x + y + z + ((x + y + z) * x1)= 276.26 2- x + 1,5y + z + ((x + 1,5y + z) * x1)= 327.35 3- 2x + 2y + 2z + ((2x + 2y + 2z) * x1)= 553 4- 3x + 2y + 2z + ((3x + 2y + 2z) * x1)= 709.74 The figures depending the equation...

I've written it out and it seems impossible. I get -50(sin^2(alpha)) = 86.63 cos(alpha) sin(alpha) - 6.54. Where would I go from there?

Homework Statement [/B] Hi, I seem to have this issue with solving the a system of 3 equations when trying to find the critical points for a 3 variable function. Homework EquationsThe Attempt at a Solution It always keeps happening. I keep getting stuck when solving these equations. Every...

Homework Statement system of equations is as follows x+y=1 2x+y-z=1 3x+y-2z=1 ##\begin{cases} x+y=1 |*(-1)\\2x+y-z=1\\3x+y-2z=1 \end{cases}## Homework Equations Gaussian elimination method technique The Attempt at a Solution ##\begin{cases} x+y=1 \\ x-z=0 |*(-2)\\ 2x-2z=0 \end{cases}##<=>...

Hey! :o A mining company produce in three mines aluminium and zinc. At the following matrix give the information about the amount of zinc and alluminium at a produced tonne of ore and the corresponding cost per tonne of ore: $$\begin{matrix} \text{Mine } & \text{ Zinc } & \text{ Alluminium }...

Find the surface in terms of a,b,c on which the following system of equations has no solution ax-2y+3z=5 -x+y-bz=-3 2x+cy-2z=d Could there be any values of a,b,c,d for which the system has infinite solution? (Justify).

1. The mb = 25 kg block is 2 m above the ledge. The pulley is a uniform disk with a radius of 10 cm and mass m = 4 kg. 2. (a) Find the speed of the 25 kg block just before it hits the ledge. (b) Find the angular speed of the pulley at that time. (c) Find the tensions in the strings. (d) Find...

Homework Statement A soccer ball is kicked. If there is a 3 meter high fence, that is 6 meters away, compute the angle of the kick and the magnitude of the velocity of a ball. Homework Equations a_y=-g v_y=-gt+v_y_0 s_y=-(1/2)gt^2+v_y_0(t) v_x is constant: we neglect air resistance. 6=v_x_0t...

Please, help with system of equations: f(x,y)=(5,-2)t+(1,1) g(x,y)=(-15,6)t+(-2,2)

Is there any general theorem on finding number of solutions to this system of equations(D e^(-k (a - t)) (1 - e^-kt) (1 - e^(-a k n)))/((1 - e^(-a k)) k t v) = S (G e^(-k (a - t)) (1 - e^-kt) (1 - e^(-a k n)))/((1 - e^(-a k)) k t v) = Twhere k,v are variables and others are constant *edited...

Homework Statement I got this question from my friend. How many real solutions for this system of equations: x2 - xy - 2 = 0 x2 + x + 2y = 0 Homework Equations Don't know The Attempt at a Solution I have never learned about this type of question. What chapter or topic should I learn in order...

I am given the following problem: Find all ordered pairs (a, b) such that ##2a + b = 12## and ##ab = 3##. Given this system of equations, I simply use substitution, and then solve the quadratic ##2a^2 - 12a + 3 = 0##. Solving this, I obtain two ordered pairs: ##\displaystyle (\frac{6 +...

So I ran into an case I have not seen before. Say we have a system of 3 equations such that W´=AW, where W=(x(t),y(t),z(t)) and A is a 3x3 matrix. The way I usually approach these is by finding the eigenvalues of A to then find the eigenvectors and thus find the ¨homogenous¨ solution. What...

Solve the system of equations $4x^2+25y^2 +9z^2 - 10xy -15yz - 6xz = 0\cdots(1)$ $x+y+z=5\cdots(2)$

Homework Statement Okay this is the problem it seems so easy but i just cannot for the life of me get it to click into my mind, I have 4 unknowns and 5 equations and i have to put it into a matrix and try solve it matricies or eigenvalues/eigenvectors. The 5 equations are: a= b/2 b=a/3 + d...

MX''=Fn(cosΦ−usinΦ) MZ''=Fn(sinΦ+ucosΦ)−Mg MΦ''=Fn(Bxx+uBz) I tried using Runge-Kutta methods to approximate motion equations in MATLAB but it turn out wrong. I also tired finding and researching forums and web for solution but to no avail. Fn,M,θ,u is constant fn/M = 0.866 it seems that i...

Prove that the system of equations below has no real solution: $x^2+y^2+z^2=1$ $x+2y+3z=4$

Homework Statement So there is a pulley with 1 mass hanging from it. The string is wrapped around and one end is taped to the pulley so that only one end of the string hangs from the pulley. There is a mass of 100 grams attached to that string. Create a system of equations to find linear...

I'm trying to answer the question below in the attachment. Could someone please check my answer to part (c), as I'm not sure. Is it correct? Is that that the right geometric explanation for the planes? (a) The equation is $\begin{pmatrix}1 & -1& 2& 1 \\ 2 & 1 & 1 & -1 \\ 1 & -2 & \lambda & 3...

Hello! I'm currently working with Maple but I do not really like the program. Is there someone with Mathematica who can run this system? $$\left \{ \begin{array}{ll} 16x^4-40ax^3+(15a^2+24b)x^2-18abx+3b^2 = 0 \\ 4x^4+5a s \sqrt{v} x^2 - 8 s \sqrt{v} x^3 - b s \sqrt{v} x > 0 \end{array}...

Homework Statement Plot the solution set of linear equations x-y+2z-t=1 2x-3y-z+t=-1 x+7z=8 and check if the set is a vector space. 2. The attempt at a solution Augmented matrix of the system: \begin{bmatrix} 1 & -1 & 2 & -1 & 1 \\ 2 & -3 & -1 & 1 & -1 \\ 1 & 0 & 7 & 0 & 8 \\...

Homework Statement So I have the following : AX=B, where $$A=\begin{bmatrix} a_{ij} \end{bmatrix}_{mXn}$$ with $$a_{ij}=i$$ $$ X=\begin{bmatrix} X_{1} &X_{2} &X_{3} &... &X_{n} \end{bmatrix}^T$$ and $$B=\begin{bmatrix} 1 &2 &3 &... &m \end{bmatrix}^T$$ Homework Equations Gauss'...

Hi, I'm looking for the real solutions to the system \begin{array}{rcl} 1 & = & v_1+v_2+v_3+v_4+v_5 \\ 1 & = & v_1^2+v_2^2+v_3^2+v_4^2+v_5^2 \end{array} Background: I'm looking at a Newton's cradle with 5 balls, each of mass ##m=1##. The first ball is pulled away and let go such that it hits...

Hello! I have the following system of equations: $$\left \{ \begin{array}{rcr} \mu^4+6 \mu^3 \delta^2 + 3 \delta^4& = &\frac{(k-3)}{s} \sqrt{v}(\mu^3+3\mu \delta^2)\\ \mu^4+10\mu^2\delta^2+15\delta^4 & = & \frac{v}{s}(w-10s)(\mu^2+3\delta^2)\end{array}\right.$$ The goal is to find $\mu$ and...

Homework Statement this is actually one of the physics problems and I have boiled down the numerical to two equations. But I have trouble manipulating equations Homework Equations Tsin(theta)=Fcos(theta)-mg and Tcos(theta)=(mv^2/Lcos(theta))-Fsin(theta) F and T are the two unknowns The...

Homework Statement find the solutions to the following system, depending on the value of the parameter l∈ℝ: lx+y+z=1 x+ly+z=l x+y+lz=l2 Find the value of λ∈ℝ for which the following system of linear equations has infinitely many solutions, for such value of λ write down all solutions: x - 2z...

Homework Statement Consider the polynomial ##p(x) = x^4 + ax^3 + bx^2 + cx + d##, where a, b, c, d ∈ ℝ. Given that 1 + i and 1 - 2i are zeroes of p(x), find the values of a, b, c and d. Homework EquationsThe Attempt at a Solution Since 1 + i and 1 - 2i are zeroes, I believe it follows that 1...

Homework Statement dNa/dt = -Na/Ta where Na is the function and Ta is the constant dNb/dt = Na/Ta - Nb/Tb where Nb is the function and Tb is the constant Homework Equations My Prof said Nb(t) has the form Nb(t) = Cexp(-t/Ta) + Dexp(-t/Tb) The Attempt at a Solution I know the first equation...

Homework Statement I need to derive the equation related to the Compton Effect from the equations for momentum and energy conservation. Homework Equations (1) Compton Effect: λ' -λ = h/me(1-cosθ) (2) Conservation of Momentum (x-direction): h/λ= (h/λ')cosθ+γumeucosΦ (3) Conservation of Momentum...

Homework Statement Below are four equations, with the known quantities listed. Solve these equations to obtain an expression for ##T## in terms of known quantities only. Do the same to obtain an expression for ##a## ##T-f=m_1a\hspace{5mm}N-m_1g\cos\theta=0## ##m_2g-T=m_2a \hspace{5mm} f=\mu N##...

I am new to this site and am not all that great at math but am trying to grow. I can't figure out how to work these equations.1) x + y + z = 15 5x - z = 18 4y + z = 19In this one I need to solve for the variables. the answers for x, y, z are 5,3,7 2) l1 + l3 = l2 5.2l1 - 3.25l2 = (-12.35)...

Solve in real numbers the system below: $a(b+c-a^3)=b(c+a-b^3)=c(a+b-c^3)=1$

"Two planes leave a city for another city that us 600 miles away. One of the planes is flying 50 miles per hour faster than the other. The slower plane takes 2 hours longer to reach the city. What is the rate of each plane? Write and solve a system of equations." My daughter is well aware that...

I have the following system of equations with variables ##a,m##, and I'm wondering—can this system be solved symbolically/analytically? \begin{align} m &= 100 + \frac{ \left( 200 \frac{\ln{\frac{1}{2}}}{26.8} \right) }{\left(\dfrac{\ln{\frac{1}{2}}}{26.8} + a \right)} \\ \\ 50 &= me^{-a\left(...

Homework Statement Solve 2x''+3x'+40x = 40y+3y' Homework Equations y = 0.05sin(10t) The Attempt at a Solution I used the annihilator method to find the answer of x(t) = Acos(10t)+Bsin(10t)+Ce-0.75tcos(sqrt(311)/4t)+De-0.75tsin(sqrt(311)/4t) where A, B, C and D are constants. The initial...

A jar contains nickels, dimes and quarters. There are 1469 coins in the jar totaling $191.25. Assuming that the number of dimes is exactly twice that of the number of nickels, how many (each) nickels, dimes and quarters are there in the jar?We were suppose to be using matrices to solve this, it...

Hi, I have two equations and two unknowns which I need to get the relation T1/T2 from. The first one is ##T1-T2=(mg)/(cos(a))## and the second one: ##T1+T2=mw^2L## I need to solve for both T1 and T2. And if I add the bottom one to the upper I should eliminate T2. But what happens with the...

Show that the following system of equations have no real solutions: $a^2+bd=0$ $c^2+bd=0$ $ab+bc=1$ $ad+cd=1$

I am trying to solve the system of simultaneous equations: \frac{\partial \rho_f\phi}{\partial t}+\frac{\partial}{\partial z}(\rho_f\phi v_f)= \frac{\partial F}{\partial t} \frac{\partial \rho_s(1-\phi)}{\partial t}+\frac{\partial}{\partial z}(\rho_s(1-\phi) v_s)=-\frac{\partial F}{\partial t}...

Hi MHB, This problem has been one big headache for me and I failed miserably every time that I attempted it. I thought to dump it into the trash, but I couldn't, simply because I would like very much to solve it. So, I hope to get some good help from this site and I thank anyone who wants...

Find all values of h and k such that the system has no solutions, a unique solution, infinitely many solutions hx +6y =2 x (h+1)y =2k I can't seem to augment the matrix. Am I allowed to multiply buy variables h / k? I can find the determinant: h^2 +h -6 Then make it equal to 0 and solve; h =...

you are laying the yellow and green brick road. the road is 1m wide and each brick is 500mm x 250mm. there are 3yellow bricks for every green brick. the road will be built with 12000 yellow bricks .how long will the road be? Let x represent the no of yellow bricks Let y represent the no of...

Homework Statement I keep getting the wrong answer, and wolphram seems to back me up. Here's the system of equations ##(-10+s)X(s)-7Y(s)=\frac{10}{s}## ##X(s)+(-2+s)Y(s)=0## Homework EquationsThe Attempt at a Solution Using Cramer's rule I've got...

Find k to have a solution? x-3y=6 x+3z=-3 2x+kx+(3-k)z=1LATEX