Linear equations Definition and 239 Threads

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...

Homework Statement For which value of alpha does the following system of linear equations have a solution? x + y = 2 x +αy = -1 αx + y = 1 The Attempt at a Solution I put it into a matrix that looks like this: 1 1 | 2 1 α | -1 α 1 | 1 Then I subtracted row1 from...

Homework Statement (1+x2)y'' - 4xy' + 6y = 0 Homework Equations I'm going to assume y can be written as [n=0 to ∞] ∑anxn The Attempt at a Solution y = [n=0 to ∞] ∑anxn ----> y' = [n=0 to ∞] ∑(n+1)an+1xn ----> y'' = [n=0 to ∞] ∑(n+2)(n+1)an+2xn ---->...

Hello, I'm a senior mechanical engineering student. I'm trying to write an application that plots the system response for a given block diagram in frequency domain just for fun. Take the system shown on the attachment for example. What I have in mind is to find the Y/U transfer function...

Homework Statement [I'm going to write column vectors as the row vectors transposed, since I don't have a fancy-schmancy equation-writing program] Consider the vectors x(1)(t)=(t 1)T and x(2)(t)=(t2 2t)T (a) Compute the Wronskian of x(1) and x(2). (b) In what intervals are x(1) and...

The solution of the system ax + ay - z = 1 x - ay - az = - 1 ax - y + az = 1 is (x,y,z) = (a,b,a). If a is not an integer, what is the value of a + b. A) -3/2 B) -1 C) 0 D) 1/2 E) 1 Can anyone help I don't know how to approach thisOk then you get : a^2 + ab -a = 1 a - ab - a^2 = -1 a^2 - b...

Hi, I wondered if anyone can help. I have some linear equations in which I've found various possible solutions to the variables using NSolve function. For example, for x1, x2, x3 and x4, it has given me ~14 different possible combinations for each x. Is it possible to do a count so if the...

Homework Statement Verify that the differential operator defined by L[y] = y(n) + p1(t)y(n−1) +· · ·+ pn(t)y is a linear differential operator. That is, show that L[c1y1+ c2 y2] = c1L[y1] + c2L[y2], where y1 and y2 are n times differentiable functions and c1 and c2 are arbitrary...

Homework Statement For part 1 I solve the problem and I got the follow equation and results: .25x+.10y+.05z=1.15 x+y+z=9 -2y+z=0 The solution is x=3, y=2, z=4 Now I have to solve this by hand with the equation in matrix form using elimination matrix Homework Equations EAx = Eb The...

Homework Statement Find a system of linear equations, with 3 unknowns, given that the solutions are the points (1,1,1) and (3,5,0) on a line. Homework Equations None The Attempt at a Solution A solution that lies on a line tells me that I'm looking at the line of intersection...

Gday, Just trying to work out the following linear differential equation. I'm trying to work it out via the Integrating Factor method and I am getting stuck at the point where you multiply both sides by I(x). The equation is: xy' - 2y = x2 Can anyone help me out with this? Regards...

When we solve for a variable in say two linear equations, by what property we are allowed to add one equation to the other or subtract one equation from the other? How can this be allowed when the two are completely different equations? For more than two equations, does this work for...

Homework Statement Solve the inhomogeneous differential equation dX/dt=AX+B in terms of the solutions to the homogeneous equation dX/dt=AX. Homework Equations A is an nxn real or complex matrix and X(t) is an n-dimensional vector-valued function. If v is an eigenvector for A with...

The simultaneous linear equations mx+12y=24---------------1 3x+my=m------------------2 have a unique solution for m= ? The answer should be m Є R\{-6,6} what I tried doing was substituting the 2nd equation into m, expanded, grouped them and factorised but I struck a...

I understand how to solve a normal second order linear equation, but this question in the homework is a bit more theoretical and I'm a bit confused. "Suppose y1(t) and y2(t) are solutions of y'' + py' + qy = 0 Verify that y(t) = k1y1(t) + k2y2(t) is also a solution for any choice of...

Hi all, I'm looking for a an effective technique for solving a system of linear equations. It should always converge, unlike jacobi or gauss seidel etc. It has to be more efficient than ordinary gauss elimination or kramers rule for large matrices. Thanks!

I have a system of linear equations which can be expressed as XA=Y where X and Y are row vectors. The vector Y and the matrix A are given. I need to solve for X. I can rephrase the same equation as AtXt=Yt but the answer will still be the same. I try using MATLAB to solve for X using the...

Homework Statement Find coefficients a, b, c, d so that the circle with the following 3 points satisfies the equation: ax^{2} + ay^{2} + bx + cy + d = 0 Points: (-4, 5) (4, -3) (-2, 7) Homework Equations The Attempt at a Solution I'm wondering if since I can only...

Homework Statement (2e^y -x) dy/dx = 1 Homework Equations dy/dx + P(x)y = Q(x) The Attempt at a Solution I know how to solve these equations, but I can't get this into the dy/dx + P(x)y = Q(x) form. In addition to this problem, is also this: (x + y^2)dy = ydx (can't get into...

Homework Statement For what values of a does the system (a-1)x + 2y = 0 2x + (a-1)y = 0 have a nontrivial solution? Homework Equations The Attempt at a Solution Argh... I'm really bad at linear algebra, can't seem to grasp the concepts. I know that if I make this into a matrix \left[...

Proof of a system of linear equations! Homework Statement Prove that if more than one solution to a system of linear equations exists, then an infinite number of solutions exists. (Hint: Show that if x1 and x2 are different solutions to AX=B, then x1 + c(x2-x1) is also a solution, for every...

Show that if u and v are solutions of the linear system Ax = b, then w = 1/4 u + 3/4 v is also a solution of Ax = b.

Homework Statement See image. a) and b) have been solved. The problem is c) Homework Equations The Attempt at a Solution I really have no idea where to begin. For the three systems given there are solutions x in range(A) for system 1 and 2 but not for 3. Therefore I have been...

Okay, so I expanded the brackets and simplified the equation from (x+4)(x-4)(x-4) to equal x3-4x2-16x+64 and I needed to sub those values into this equation y=ax3+bx2+cx-d where a=x3 b=-4x2 c=-16 d=64 which were the values I got from the first equation. I need confirmation If it would be...

I'm having some trouble getting my head around the concept of multiple solutions of differential equations of higher order, that is the general solution to a linear homogeneous equation is a linear combination of constants and solutions like y(1)C1 + y(2)C2 +y(n)C(n) where N is the order of the...

1. You have a system of equations of the following form: x + iy = 0 -ix + z = 0 y - z = 0 or -2Sqr(5)x - iy = 0 ix - 2Sqr(5)y + 2iz = 0 -2iy -...

Homework Statement Prove that the equation \left( \begin{array}{ccc} 1 & 2 & -3 \\ 2 & 6 & -11 \\ 1 & -2 & 7 \end{array} \right)\left( \begin{array}{c} x \\ y \\ z \end{array} \right)=\left( \begin{array}{c} a \\ b \\ c \end{array} \right) Is only soluble if...

Homework Statement For a few problems dealing with eigenvectors, I substituted my eigenvalues into the characteristic equations. I got systems of linear equations. I need to find the general solution to the systems in order to find the corresponding eigenvectors. For example in one problem...

http://peecee.dk/uploads/042009/Screenshot4.png I have to find (a,b) \in R when the system of linear equations a) have no solution b) have one solution c) have infinitely mane solutions. I've converted the equations so they're on a row echelon form. My question is, what do I do from here?

Hey guys, For my assignment, I have choose any engineering or science problem which requires the solution of at least three nonlinear simultaneous equations, and code it into Matlab. The problem is that I cannot find a simple real world problem that needs a nonlinear system of equations...

Homework Statement Find the general solution of \frac{dy}{dt} + 2y = 3t^2 + 2t -1 Homework Equations The Attempt at a Solution So just worrying about the right side y_p = at^2 + bt + c so \frac{dy_p}{dt} + y_p = 2at + b +at^2 + bt + c = 3t^2+2t - 1 at^2 = 3t^2...

Homework Statement I wish to solve the following two equations, which are related: h(x,y) = y \quad \text{and} \quad g(x,y) = y+x^2-bx. First I set h=0, which gives me y=0. Then I insert y=0 in g, where I find x=b and x=0. All is good here. ********* Now I wish to solve the same system...

Delete please Please delete. (Edited on Friday 13th 2:53 p.m.) Homework Statement ANYTHING that looks similar to solving these by addition/elimination: Equation One: 3x - y + 2z = 1 Equation Two: 2x +3y +3z = 4 Equation Three: x + y - 4z = -9 The book's answers: (-1, 0, 2) The...

I am currently taking the first college level linear algebra course and have a question. Consider the system of equations: 1 3 2 |1 0 -4 5 |-23 2 2 9 |t Find values of t for which solutions to this augmented matrix can be obtained. Explain the implications of this...

Homework Statement Find out if the following system of equation has solution. In case of having solutions, describe parametrically them all and give 2 of them explicitly. 2x-z=4 x-2y+2z=7 3x+2y=1 2. The attempt at a solution I don't see nowhere in my notes what they want by...

Consistency of non-homogenous systems of linear equations Hello, Is it possible to find out if a non-homogenous system of linear equations has: - Single Solution. or - Infinite Solutions. or - No Solutions. Without applying any methods/rules ( Such as Gauss, determinant..etc), just...

Solve a system of linear equations Ax=kb A is a matrix with m*n elements, A = \left[\stackrel{a_{11}\; \ldots \;a_{1n}}{ \vdots \ \ddots \ \vdots} {a_{m1}\cdots a_{mn} \\} \right] \sum _{j=1} ^{n}a_{ij}=1 ,0\leq a_{ij}\leq1, 1\leq i\leq m,1\leq j \leq n , m > n b is a vector with m*1...

Homework Statement Taking first year matrix/linear algebra theory at college. I got a system of linear equations: x+2y+3z=0 -5y-2z=0 4z=0 2. The attempt at a solution This question looks so funny and easy but I think there must be a trick answer. I got: z = 0, y = 0 and...

Hey, I am very new at using matrices to solve systems of equations. My question isn't actually how to invert a matrix or anything, its much simpler. Homework Statement If you add the age of 6 people, Anna, Barbara, Cathy, Dan, Eric, Fred, the total is 92. Anna is twice the age of Cathy...

Homework Statement Given augmented matrix \left(\begin{array}{ccc}a&1&-1\\2&1&b\end{array}\right) list conditions on a and b such that there is: i) no solution ii) infinitely many solutions and iii) a unique solution The Attempt at a Solution I row-reduced the matrix to...

how would i get it to solve linear equations and linear systems, especially in the form; y=ax+b my professor and i found out that it likes brackets " [ . . . ] " and double equal signs " == " i know its probably painfully obvious but any input would be tremendous!

Homework Statement This is from Further Pure Mathematics by L. Bonstock S. Chandler and C. Rourke (question 11 pg 113). The question is find the set of points which are mapped to the point (1, -1, -1) by the transformation \left( \begin{array}{ccc} 1 & -2 & 4 \\ 3 & 4 & 6 \\ 1 & 3 & 1 \\...

Can anyone help me to learn how to solve systems of linear equations? {-5x-5y=-5 {-40x-3y=2 How do I go about doing this using the addition method?

Homework Statement The figure attached shows a network of one way streets. On a particular day the traffic flow was measured at each of the intersections a b c and d. The numbers in the figure represent the average number of vehicles per minute through the four intersections. A) Set up and...

Hi, So I am going over on how to find a geodesic from any metric, esp. on a 2-sphere. I have been looking at my lecture notes and am confused as to how my professor solves for the equation in terms of the variables, i.e. (\theta , \phi) . If i use the 2-sphere as an example here where the...

solve each system of linear equations. Indicate whether each system is inconsistant, dependent, or independent. i'm not sure how to get these problems into slope intercept form: y=mx+b 1. 3x - 6y=9 1/2x=y +3/2 2. 2x + 3y=1 -3x + 4y=-10 3. 0.5x - 0.75y=0.125 4x-6y=12 if...

...Can someone refresh my memory; what do you call a linear equation that does not lie in a single plane? Can you give me an example; or two? I come across the term in passing; in a book on Linear equations; that brought them up only to say that it wouldn't be covering them. I don't have the...