Linear equations Definition and 233 Threads

Dear All, I have a linear system of equations such as Ax = b where A is a m-by-n matrix and m < n and A is a full rank matrix (rank(A) = m). Since there are infinitely many solutions to this problem, I was looking for different methods to solve this problem. As I understood I can pose this...

Find all solutions to the following system of linear equations: (x1) – 2(x2) – (x3)+(x4)=1 2(x1) – 3(x2) + (x3) – (x4)=6 3(x1) – 3(x2) + 6(x3))=15 (x1) + 5(x3)+(x4)=9 Using a system of linear equations, I found: 1 -2 -1 0 1 0 1 3 -3 4 0 0 0 6 0 0 0 0 0 0 so three solutions are...

Hello, I'm trying to solve a differential equation with boundary conditions which leads me to an infinite system of linear equations. I can obtain an approximate solution of the problem just by considering only the first n terms so I have a system of n equations with n unknowns. I've been...

Homework Statement A store sells cashews for $5.00 per pound and peanuts for $1.50 per pound. The manager decides to mix 30 pounds of peanuts with some cashews and sell the mixture for $3.00 per pound. How many pounds of cashews should be mixed with the peanuts so that the mixture will...

Homework Statement Suppose that y(x) is the solution to the initial problem, y'=y(1-x), y(1)=e find y(2)Homework Equations The Attempt at a Solution This is my initial attempt: \frac{dy}{dx}=y(1-x) \frac{dy}{y}=(1-x)dx i then integrated both side to get: lny=-ln(1-x)+C and here's the problem...

Hi everyone! 1. Is a linear equation the same as a polynomial of first(or 0th) degree? 2. The book 'Mathematics for physicists and engineers' by springer(publisher) states that an example of a linear (DE) equation is 5.dy(x)/dx = x.y(x). Yet I read somewhere else that f(x,y)=a.x.y+b is not...

hi all, Which is the fastest algorithm for linear equations in the form of A*X = B. Where A can be a symmetric or sparse matrix and also bear in mind that A matrix is huge in size something like 5000x5000. Regards,

Homework Statement Does the following set of linear equations have a unique solution? (excluding any trivial solutions when x=y=z=0) Do not attempt to formally solve the equations. x+2y-4z=8 4x-6y+12z=19 -6x+3y-6z=-20 Homework Equations The Attempt at a Solution...

I'm taking a step back as I've found a concept I'm struggling with. If I have an equation: 2(x-1)/3 = (x/4)+1 I've been told I need to multiply by 12 to give me: 8(x-1) = 3x+12 However I'm struggling with the multiplication of fractions in his instance. Can anyone advise me how that...

1)Determine whether the given statement is true or false. A homogeneous linear system with the same number of equations as unknowns always has a unique solution. 2)Determine whether the given statement is true or false. If a linear system has no solution, the rank of the coecient matrix...

Source: http://en.wikipedia.org/wiki/Linear_equation General form:- It says (under the title General Form) "If B is nonzero, then the y-intercept, that is the y-coordinate of the point where the graph crosses the y-axis (where x is zero), is −C/B, and the slope of the line is −A/B."...

how can i solve x1 + x2 = 5 2x1 + x2 = 4 using simplex method? thanks

Homework Statement "Determine the currents in the various branches" Homework Equations The one I am stuck on is 6. The Attempt at a Solution I know there is 3 equations, I believe one of them is I1 + I2= 3 and a second is 4= 2I3+I2 ?? but I am not sure if that is correct...

If I were to solve a system of multiple equations in the form αx+βy+ζz=p_{1} Where α,β,ζ are constants x,y,z are variables, and p is a prime, how would I use Galois theory and/or number theory to find the number of solutions if the other equations could all be written in the form...

Homework Statement Systems of first order equations can sometimes be transformed into a single equation of higher order. Consider the system (1) x1' = -2x1 + x2 (2) x2' = x1 - 2x2 Solve the first equation for x2 and substitute into the second equation, thereby obtaining a second order...

So we did a lab in class using an inclined air table, two pucks and a spark timer. Only one puck was used and we "launched" it in a way that when the spark timer was activated, it traced a parabola on the sheet of paper over the air table. What I don't understand is: why is horizontal...

Hello, I am in need of explinations on how to resolve second degree linear equations with a constant. I had a maths test last saturday and this was the last question : Resolve y"+3y'+2=cos(t) Having almost fallen into the trap of resolving y"+3y'+2y=cos(t), I passed the 2 over by cos(t)...

Homework Statement Given that the values for a, b, c, d, e and f for the system ax+by=e, cx+dy=f has two different solutions. Show that ax+by=0, cx+dy=0 also has two different solutions. Homework Equations The Attempt at a Solution There're three cases of how two straight lines...

http://www.scribd.com/doc/66759813/mat223tut1" Question 2 and 3 Homework Statement For what values of c does the system have no solutions? I figured out the other ones, for c=0 we can assign a parameter to x1 and it will then have infinite solutions. For c=1 the system will have a unique...

Homework Statement x=.5x + .3y +.2z y= .4x + .4y + .3z z= .1x + .3y + .5z x+y+z=1 Homework Equations when solved, x= 21/62, y=23/62, z= 18/62 The Attempt at a Solution I've tried doing row reduction but I keep failing ex: .5 .3 .2 .4 .4 .3 .1 .3 .5 = 0 -1.2 -2.3 .4 .4...

My book stated the following theorem: If the functions P(x) and Q(x) are continuous on the open interval I containing the point x0, then the initial value problem dy/dx + P(x)y = Q(x), y(x0)=y0 has a unique solution y(x) on I, given by the formula y=1/I(x)\intI(x)Q(x)dx where I(x) is the...

I am doing my Extended essay about the maths involved in calculating your position using the GPS. I am reading a very complete book, but the maths are sometimes too hard or not enough deeply explained for my level and I am struggling to follow some parts. Here I post one page of the book where...

Homework Statement For which real numbers  does the following system have a unique solution? 14x - 6y + 18z = 2\lambda z x = \lambda x 3x - 8y = -\lambda y Homework Equations The Attempt at a Solution hi, I rearranged the equations...

Homework Statement \lambda x_1 +x_2=1 x_1 +2\lambda x_2+x_3=2 x_2 +\lambda x_3=1 The Attempt at a Solution The determinant is 0 for Lambda=0 and 1, found the infinite solutions associated with those to be (1,0,1)+t(-1,1,-1) and (0,1,2)+t(1,0,-1) I need to show a...

Hi, I hope this is going in the proper place, its essentially maximizing a matrix so here goes: Given the independant variables a, b, c, d, and e, and the system [ 1 1 0 5 1 | A ] [ 0 3 0 1 1 | B ] [ 4 1 1 0 1 | C ] [ 1 0 3 1 0 | D ] I want to find the a, b, c, d, and e that will...

Homework Statement Row A) x1 + 2x2 - x3 + x4 + 2x5 = 1 Row B) 2x1 + x2 + x3 - x4 + 2x6 = -1 Row C) x1 + 4x2 - 2x3 + x4 - x5 = 0 Row D) x1 + x2 + 3x3 + x4 + x6 = 2 Homework Equations Ri <--> Rj Ri --> cRj, c not equal to 0 Ri --> Ri + cRj, c \neq 0, i \neq j The Attempt at a...

Say we can find a solution to the Schrodinger equation, which gives a superposition of two states x1 and x2. Say this occurs at time0. The equation evolves over time, say to time1. At time1, are x1 and x2 (the same states found by solving the Schrodinger equation at time0) still...

Homework Statement for the system of linear questions given as l 2 1 -5 l l x l= l 1 l l -1 -3 h l l y l= l 2 l Find all values for h for which the system will have no solution l -3 2 6 l l z l= l 3 l Homework Equations The Attempt at a Solution

what does a homogeneous linear equation in 3 variables represent geometrically ?

while solving 3 linear equations in 3 variables by cramer's rule if all the determinant's are 0 then what can we conclude?

Homework Statement A doctor's prescription calls for a daily intake of liquid containing 40mg of vitamin c and 30mg of vitamin d. There are three liquids that can be used: one contains 20%vitamin c and 30% vitamin d; the second, 40% vitamin c and 20% vitamin d; the third, 30% vitamin c and 50%...

Let C1 and C2 be circles in the plane. Describe the number of possible points of intersection of C1 and C2. It is 4?

1) Is the matrix [upper row 3 0 and lower row 0 2] a linear combination of the matrices [upper row 1 0 and lower row 0 1] and [upper row 1 0 and lower row 0 0]? Justify your answer. Is it I just have to add the two matrices to see if they are equal the matrix, [upper row 3 0 and lower row 0...

solve each given linear system by the method of elimination 2x-3y+4z=-12 x-2y+z=-5 3x+y+2z=1 How to solve this problem. What should I do first?

Homework Statement Let W be the subspace of R4 such that W is the solution set to the following system of equations: x1-4x2+2x3-x4=0 3x1-13x2+7x3-2x4=0 Let U be subspace of R4 such that U is the set of vectors in R4 such the inner product <u,w>=0 for every w in W. Find a 2 by 4...

Note: I didn't use the template because I feel it did not fit the question well enough. This is concerning a system of linear equations in two variables where its constants in " ax+by=c " form show a geometric sequence, i.e. " nx + any = a2n ". Another way of putting this is " y=(-1/a)x + a...

Homework Statement How do I show that a system of linear equations either has a solution or has multiple solutions? Homework Equations Show that the system of equations a*x _{1} + 2*x_{2} + a*x_{3} = 5a x _{1} + 2*x_{2} + (2-a)*x_{3} = 5a 3*x _{1} + (a+2)*x_{2} + 6*x_{3} = 15 is...

Homework Statement Suppose you have points of a specific form, say (x, y, 3x + 2y). Show that this set of points is a solution to a homogeneous system of linear equations, hence a subspace. The Attempt at a Solution I'm wondering how one is able to go about this. Here's my try, but I'm not...

Consider a certain linear system of 2 equations x'=Ax. Suppose the real-valued coefficient matrix A has r=-1+4i as one of its eigenvalues, and that one of its corresponding eigenvectors is (2, 5-2i). Find the particular solution that satisfies the initial condition x(0) = (-4, 3)...

If you have, as an example, a 3x3 matrix: A = { {1, 2, 3}, {4, 5, 6}, {7, 8, 9} } Such that Ax = 0 and you perform row reductions on it and at a certain point it reduces to: { {1, 2, 3}, { 0, 1, 2}, {0, 1, 2} } Then you could legitimately remove one of {0, 1, 2} from the system...

Homework Statement Exercise 1: For what value of m will the following system of linear equations have infinitely many solutions? mx + 3y = 12 2x + (1/2)y = 5 Exercise 2: For what value of k will the following system of linear equations x + 2y + kz = 1 2x + ky + 8z = 3 have a) unique...

Hi guys, so I have this system of linear equations: x' = -3x - 1y y' = 3x - 7y And I'm supposed to decouple them by this linear change of variables: z = Ax + By w = Cx + Dy I'm supposed to find values for A, B, C, and D and I have no idea where to begin. Can anyone walk me through...

Hello! Quick and silly question; my apologies, but it shouldn't take to long to answer! Is a set of x linear equations the same as x simultaneous linear equations? I'm pretty sure they are, but are there any nuances I'm overlooking? Is there any thing that can be considered one but not the...

At 11AM a train traveling 57 mph leaves Chaney City for Atlantic City 543 miles south. At 1PM a train on a parallel track leaves Atlantic City for Chaney City and travels at 42 mph. At what time will they pass each other? I have 57x+42y=543 and x+2=y and I solved for x and y. I got x=51/11...

Hello! I was wondering about inconsistencies in linear equations. If I have three equations and four unknowns, and I can make one a linear combination of the other two, then I can identify if there is an inconsistency. If I cannot make one from a linear combination of the other two, how do I...

Proving a linear system of equations cannot have more than one finite solutions Homework Statement Prove that the number of solutions to a linear system can not be a finite number larger than one. Provide either a general proof or for a system with two equations and two unknowns...

Homework Statement This is from a solved problem: So, how did they get this solution? I tried solving this and I just don't get it! The Attempt at a Solution The matrix corresponds to the set of equations: x=0 -x=0 3x-5y=0 If I take "y" to be the free variable, I have...

Homework Statement Let A=[{1,3,2,2},{1,1,0,-2},{0,1,1,2}] i) Find the rank ii) Viewing A as a linear map from M4x1 to M3x1, find a basis for the kernel of A and verify directly that these basis vectors are indeed linearly independent. Homework Equations None The Attempt at a Solution...

Homework Statement Determine whether the following planes are parallel or intersect. If they intersect, find the equation of the line of intersection. Interpret this system of two linear equations geometrically. 4x - 3y - z - 1 = 0 and 2x + 4y + z - 5 = 0 Homework Equations The...

Homework Statement Find the equation of the plane that passes through the line of intersection of the planes 4x - 3y - z - 1 = 0 and 2x + 4y + z - 5 = 0 and parallel to the x - axis. Homework Equations The Attempt at a Solution The equation of the plane...