Linear equations Definition and 233 Threads

Homework Statement I'm given a system of equations and I'm told to: Solve this system by hand in 4-decimal digit arithmetic with rounding, using Gaussian elimination without pivoting and backward substitution Homework EquationsThe Attempt at a Solution When they say 'without backward...

Homework Statement 2 women and 5 men can finish a work a work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 women alone to finish the work, and also that taken by 1 man alone.Homework Equations Pair of linear equations in two variablesThe Attempt at a...

When talking about ordinary (real) linear differential equations with constant coefficients the idea is that we are dealing with the vector space of real functions over the field of real numbers. But when we allow the coefficients of a linear differential equation to be functions are we dealing...

Hello all, I need your help, I am trying to put some order in all the possible outcomes of a system of linear equations, I want to create a diagram or a table for my convenience. What I want to know, which I am not sure of, is these kind of things: If the system is homogeneous, and there are...

Right, i don't believe this is a homework question. The only reason I am stating this is because PF are stringent with their rules. I'm quite confused and I'm not sure how to explicitly state my problem. The vertices of a triangle are (a,b) (c,d) and (e,f). This can be arranged into a...

Hello (Nod) Can someone help get me started on this problem? Like a setup or direct on how to set it up. $2xy'+y=6x$, $x>0$, $y(4)=20$

Hi, Let's say I have a function f(x) = 2*log(x). I know scientists sometimes plot f(x) on the y axis, but then instead of plotting x on the x-axis they plot log (x) such that the graph becomes linear. How would i plot a function f(x)= 2*log(x) such that it is linear ? My attemps -...

Hi, all. While solving a second order linear differential equation why do we have to use linear independent but two solutions. For example, when solving y''- y = 0 , y(0) = 5 and y'(0) = 3 , we use ex and e-x and then we write y = c1*ex+ c2*e-x-

I have a system of 379 linear equations and 6325 unknowns. Does anyone know of a tool that can generate some (non-negative) solutions that satisfy this system? I know there are infinitely many, but it would be useful just to have a few for my purposes.

Homework Statement What Hybrid Methods are used for solving linear equations and how are they advantageous to classic methods? Homework Equations The Attempt at a Solution Well I assume that more robust methods such as bisection would be combined with Newtons or secant which are...

I'm solving a plenty list of exercises about application of linear equation. Currently I have solved 97% of them correctly. But there are some items I really need help with.here are they, 1. A nugget of gold and quartz weighs 100 grams. Gold weighs 19.3 g/cm3 (grams per cubic centimeter)...

I am looking at a particular form of a set of linear equations. On the attached picture the form is shown for the case of 8 linear equations. It should not be hard to see how the set would look for an arbitrary N. My question is: Can anyone see if this special set of equations can be solved in a...

1. An object of unit mass is dropped from a height of 20 above a liquid-filled reservoir of depth 50. If the acceleration of gravity is 9.8 and the resistance-to-motion coefficients of air and liquid are 1 and 4, respectively, compute the time taken by the object to hit the bottom of the...

My problem is: A coffee house blended 18 pounds of espresso flavored coffee beans with 17 pounds of vanilla flavored coffee beans. The 35 pound mixture cost \$306.50. A second mixture included 19 pounds of espresso flavored coffee beans and 15 pounds of vanilla flavored coffee beans. The 34...

The annual sophomore class picnic is planned by a committee consisting of 17 members. A vote to determine whether the picnic should be held at the beach location or in the mountains resulted in a victory for the beach location. However, if two committee members had changed their vote from...

Every freshman student at a particular college is required to take an english aptitude exam. A student who passes the examination enrolls in english composition, and a student who fails the test must enroll in english fundamentals. In a freshman class of 1240 students there are more students...

1/5(1/3x-5)=1/3(3-1/x)

Homework Statement Solve the following system of linear equations. ##\begin{array}{cc} \frac{1}{2}x+y-\frac{3}{4}z=1 \\ \frac{2}{3}x-\frac{1}{3}y+z=2 \\ x-\frac{1}{5}y+2z=1 \end{array}## The Attempt at a Solution Can I just do elimination by addition? So if I multiple the first equation by...

Hello all, this is my first post here and I hope to get some help. I am not as good at math as most of you so sorry if this is a really easy question Homework Statement Solve for x and y: 7x-y=2 2x+2y=5 I can do these types really easy but on the next page of my book it says: Let a,b,c,d be...

Homework Statement |1 0-1-2-8 | -3| |0 0 1 2 7 | 1| |0 0 0 1 -4 | -13| I think that x_{2} is a free variable, so when writing the general solution in a solution set, what would I put for it? Nothing?

Homework Statement x + 3y + z = 4 2x + 2y + z = -1 2x + 3y + z = 3 Find the general solution, and two particular solutions. The Attempt at a Solution y = 4; x = -1; z = -7; if I am not mistaken. So how am I supposed to find a general and two particular solutions if there is only...

Hello everyone, I was just solving a problem in which I had to determine the system of linear equations were consistent. Evidently, if a system of linear equations is capable of being put into triangular form, with no contradictions present, then it must consistent. My question is, why is...

Hey! I need some help using the Matlab function ljx.m for solving a system of linear equations. I found a solved example for A= \bigl(\begin{smallmatrix} 1 & -1 &0 & 1\\ 1 & 0& 1 & 0\\ 1 &1 &2 & -1 \end{smallmatrix}\bigr) and b= \bigl(\begin{smallmatrix} 1\\ 1\\ -1 \end{smallmatrix}\bigr)...

Hello again, I have this system presented below: \[\left\{\begin{matrix} x+y+z+w=1 \\ -3x-3y+kz-kw=-2 \\ 2x+2y+2z+kw=4-k \end{matrix}\right.\] I need to find for which values of k the system has an infinite number of solutions with 2 degrees of freedom, and to find a general solution for this...

Hello, I am working on a hybrid simulation-optimization problem of a hamiltonian cycle in two-dimensional Euclidean space, and have encountered the following problem: Say I have a system of N linear equations and M unknowns, where M > N, with the following constraints: 1. Every...

Hello all, I need your help with this tricky problem. Determine the value of \[\lambda\] so that the following linear equation system of three unknowns has only the zero solution: \[\begin{pmatrix} 1 &1 &1 &0 \\ 1 &\lambda &1 &0 \\ \lambda &1 &1 &0 \end{pmatrix}\] I have started working on...

Hi guys, I'd be grateful for any help with this type of question. It's been driving me crazy. I have an online assignment for my linear algebra course and the question is always like this: "Determine the values of a for which the following system of linear equations has no solutions, a unique...

Homework Statement The problem is to find the values of x and y that solve the following system of linear equations: 6751x + 3249y = 26751 3249x + 6751y = 23249 However, the caveat is that I must contrive a mental process of solving them--I must find x and y in my head.Homework Equations The...

Homework Statement A baseball team won 54 more games than it lost. If the team played a total of 154 games and there were no ties, how many games did the team win? (A) 50 (B) 98 (C) 100 (D) 102 (E) 104Correct Answer is Homework Equations ok so no. of games won = x ... no. of games...

Homework Statement Twelve equal rectangular ceiling panels are placed in a four long by three wide grid. Each panel is 150mm longer than it is wide. Between the panels runs an edge/middle strip which totals 40.0m in total length. (This runs round the whole perimeter and between each panel)...

Hi, I'd just like to have a quick clarification with regards to the method of undetermined coefficients. I know that if a characteristic equation has the form (r-4)3 = 0 then the characteristic solution will be yc = e4t + te4t + t2e4t + t3e4t and the particular solution ought to be...

I'm probably making a silly mistake or Wolfram Alpha is lying to me. Question: Find the value of c and d. 3d=13-2c \frac{3c+d}{2}=8 Rearranged, simplified and multiply each equation by 2: 6d+4c=26 d+3c=16 Now find the common multiple which in my case I will use 12: 18d+12c=78 -4d-12c=-64...

Homework Statement Problem: A system of linear equations can't have exactly two solutions. Why? (a) If (x, y, z) and (X, Y, Z) are two solutions, what is another solution? (b) If 25 planes meet at two points, where else do they meet? Solution: (a) Another solution is 1/2 * (x + X, y + Y, z +...

Homework Statement 2x +5y -z = 3 3x + 5y -4z = -6 the bracket needs to go infront, so x,y,z satisfy all the equations at once. 4x -2y +6z = 1 Homework Equations Cramer's method: (I don't know how to add certain symbols to the text so it is difficult to express it) If A were the matrix of the...

Homework Statement For what value(s) of k does the system of linear equations below have a unique solution? 2x+(k-1)y = 6 3x+(2[I]k+1)y= 9 Homework Equations The Attempt at a Solution I'm uncertain how to even go about tackling this problem. Given how all the other problems...

Homework Statement I don't have a particular problem to solve, but I need help with understanding the notation I have found in an academic paper. I have a system of linear equations which each take the form: pi xi r1 + pi yi r2 - pi u + qi xi r4 + qi yi r5 - qi v + xi x + yi y -...

Hi guys I wonder if you know any linear algebra formalism or something to solve the following question systematically? Give A,B with A=n1xn2 matrix and B=n1xm2 matrix. How do we get C=n2xm2 matrix such that A*C=B. A simple example if A=(1,2)^t, B=(2,4)^t, then C=2 The question is how to...

Hi, I am doing self study and have hit a snag in the road. Can someone please clarfiy this for me. I am reading K.A. Stroud's Engineering Mathematics which so far has been great.Consider the equation \frac{dy}{dx} + 5y = e2x In this case, we begin multiplying both sides by e5x. This gives...

Hi, I am doing self study and have hit a snag in the road. Can someone please clarfiy this for me. I am reading K.A. Stroud's Engineering Mathematics which so far has been great. Consider the equation \frac{dy}{dx} + 5y = e2x In this case, we begin multiplying both sides by e5x. This...

Differential equations Homogeneous Linear Equations case 1 +example - YouTube There are more on my channel and will be posting more daily.

1.Determine the value(s) of k for which the system of linear equations x + 2y = 1 (k2)x - 2ky = 2 has exactly one solution 3.How do i solve this, i tried the 2x2 matrix whereby, i had |1 2| |k2 -2k| and tried to make [2 and k^2 = zero] and [-2k = one] But I can't seem to solve it completely...

Consider the system of linear equations (A+D)x=b, where D is a positive semidefinite diagonal matrix. Assume for simplicity that (A+D) is full rank for any D that we care about. In my particular case of interest, D has the form D = blkdiag(0,M) for some positive diagonal matrix M. So, a subset...

My book discusses the oscillations of systems for small pertubations around an equilibrium point. By considering taylors expansions of the potential and kinetic energy they are led to a set of equations for the amplitude factors. I have attached the crucial lines as a picture. My question is...

Homework Statement For the following system, indicate for what values of a and b the system will have i.) One Solution ii.) No Solutions iii.) Infinitely Many Solutions Homework Equations 2x + y - az = 1 5x + 3y - 2az = 2+2b x + y + az = bThe Attempt at a Solution [ 1...

Homework Statement dr/d∅+rtan∅=cos∅ μ(∅)=exp[∫tan∅] μ∅=exp[-ln[cos∅]=-cos∅ -cos∅(dr/d∅)-rtan∅cos∅=-cos^2∅ dr/d∅[-rcos∅]=-cos^2∅ rcos∅=∫cos^2∅ changed cos^2∅ to 1/2+1/2cos2∅ rcos∅=1/2∅ + 1/4 sin2∅+c the books answer is not even close to mine they have r=(∅+c)cos∅...

Hello Forum, a system of linear equations can be determined (if there are as many unknowns as equations), overdetermined or underdetermined. In general, is it easier to solve an overdetermined or an underdetermined system? Am I correct in thinking that both have an infinite number of...

Einstein, in his paper "On the Electrodynamics of Moving Bodies", part 1, sec. 3, writes: "Primarily it is clear that on account of the property of homogeneity which we ascribe to time and space, the equations must be linear." What has the homogeneity of space and time to do with the degree of...

If the system of Linear Equations x+y+z=6 x+2y+3z=14 2x+5y+\lambda z=\mu has infinite number of solution in x, y, z I need to find out two things 1. The value of λ 2. Maximum value of (\mu x+\lambda y-20z)sin^2\theta+(\lambda x+\mu y+64z)cos2\theta, \theta \in \mathbb{R} is 272 I used the...

Hi all, How do u go about doing this question? x - 2y +z =4 y- z =3 (a^2 - a - 2)z = a+1 Determine values of a for which the system has no solution, one solution and many solutions Stephen

Homework Statement Suppose that you are the manager of a sheet metal shop. A customer asks you to manufacture 10,000 boxes, each box being open on the top. The boxes are required to have a square base and a 9 cubic foot capacity. You construct the boxes by cutting out a square from each...