Linear equation Definition and 131 Threads

Homework Statement Solve these linear equations: Homework Equations \frac{x-4}{6} - \frac{x+5}{3} = \frac{4-x}{2} The Attempt at a Solution \frac{x-4}{6} - \frac{x+5}{3} = \frac{4-x}{2} Multiplied by 6 \frac{6x-18}{6} - \frac{6x+30}{3} = \frac{24-6x}{2} Simplified x-18-2x+30 =12-6x Group...

Have I got this linear equation right? 8y - 31 = 13 - 3y My answer is y = 8.8

Homework Statement I just have a general question. Suppose a,b and c are integers with a and b not both 0. There exists d=gcd(a,b) and ax+by=c. From this I know that d|a and d|b but how do I know that there exists x,y such that d|(ax+by) where ax+by does not equal d and d|c ? I cannot...

Let E = span{v1, v2} be the linear subspace of R3 spanned by the vectors v1 = (0,1,-2) and v2 = (1, 1, 1). Find numbers a, b, c so that E = {(x, y, z) of R3 : ax + by + cz = 0} I tried doing this question, but I am totally lost. I know that any vector in E can be represented as a linear...

please help me to solve linear equation in matrix form if determinant is zero

1. I thought I was doing it right, but Quest said I have to wrong answer. Can some one solve it in steps and produce a final answer so I can compare? Tan 58=(vi-ayt)/axt where vi=5.6 ay=-9.8 ax=2.1 solve for t. I got 0.87 for t. Thank you.

1. I thought I was doing it right, but Quest said I have to wrong answer. Can some one solve it in steps and produce a final answer so I can compare? Tan 58=(vi-ayt)/axt where vi=5.6 ay=-9.8 ax=2.1 solve for t. I got 0.87 for t. Thank you.

1. I am having a trouble with this math problem and would like help finding the answer. Here goes: Let (the ~~ indicates where a line should straight line should be going downward and /// are like a space between the numbers) 1 /// (-1) /// 1 ~~ 2 a ///...

Homework Statement Solve the system of the linear equations and interpret your solution geometrically: 2x + y + 2z - 4 = 0 [1] x - y - z - 2 = 0 [2] x + 2y -6z - 12 = 0 [3] The Attempt at a Solution I've tried to eliminate the y variable: [1] + [2] 3x + z - 6 = 0 [4]...

Homework Statement I'm sure this is easy but I've been looking at it for an hour and can't get anywhere. I have an equation that I need a linear form of. Homework Equations y = a*b*(x1*x22-(x3*x44/c))/(1+b*x1) That's the equation I have to write a linear form of. The Attempt at a Solution...

First Order Linear Equation I have a question about differential equations... The equation for a general linear differential equation that is: dy/dx + P(x)y = Q(x) So my question is can you have a Q(x) that has both x and y variables? For Example: dy/dx + (1/x)y = (1/x)y^2

What do I do when a decimal or a fraction is found only within the parentheses in a linear equation? I know about the general removal process; but my question involves equations like these: 17(2.33 - x) - 35(4 - 30x) = 2 7(4/3 - x) + 24(5x - 60) = 31 Should I distribute first and then get...

give an example for a set of linear equation (from field R) that has the following general solution: http://img244.imageshack.us/img244/5226/26420883un6.gif ??

Homework Statement Suppose the system below is consistent for all possible values of f and g. What can you say about the coefficients c and d? Homework Equations x1 + 3x2 = f cx1 + dx2 = g The Attempt at a Solution I really just have no idea what this says about c and d.

I found a rule that the equation ax + by = (a-1)(b-1), for gcd(a, b)=1, has a solution in integers x and y with x ≥ 0 and y≥0, but the equation ax + by = (a-1)(b-1) - 1 don't. For example, the equation 3x + 7y = 12 has such soluntion (x, y) = (4, 0), but 3x + 7y = 11 has no such solutions that...

let A be a mxn matrix. prove that the system of linear equations Ax=b is consistnet for all column vectors b if and only if the rank of A is m. I have no idea how to start, can anyone helo me out?

Does anyone know of a good linear equation website? I really am having trouble following it, and I'm going to be tested on it next week. Just a site with basic problems that I can try and solve. thanks - snow

Hi! This is my first post at this forum. At the look of it I think i will be spending a lot of time here. I´ve have a problem that i need help with. Me and my boyfriend started a discussion yeasterday who was the smartest of us. So we gave each other a assignment. Mine was: Solve the...

18.1 #33 Let L be a nonzero real # (a) Show that the boundary-value problem y''+vy=0, y(0)=0, y(L)=0, has only the trivial solution y=0 for the cases v=0 and v<0. I get (a), but I don't know how to do (b) (b) For the cases v>0, find the values of v for which this problem has a...

HELLO, IN A LINEAR EQUATION OF THE FORM, X2 + Y2 + Z2 + D = 0 CAN THE PARAMETER BE -D WHERE t = parameter = -D and V = direction vector and Vt = <at, bt, ct> It seems as if it is...but I can't seem to prove it. HELP HELP HELP HELP

Hi , I am stuck with the following problem: Find a second order linear homogeneous equation having the pair as a fundamental set of solutions: y1(x)=x , y2(x)=x*ln(x). My problem here is that I don't have the exponential form for the proposed solutions. Thank you for your help B.

Can anyone help me convert this linear equation to angular terms? mx'' + f*sin(x') + kx = 0 x'' = x double dot x' = x dot Im having trouble find info on changing this.

Find all solutions \phi of y''+y=0 satisfying: 1) \phi(0)=1, \phi(\pi/2)=2 2) \phi(0)=0, \phi(\pi)=0 3) \phi(0)=0, \phi'(\pi/2)=0 4) \phi(0)=0, \phi(\pi/2)=0 I cannot seem to solve parts 2-4 in a way that...

I have been trying to brush up on linear algebra and I fear I still have a weak handle on some of the most basic concepts. For instance I am still trying to find a precise answer to the question, "is this function linear?" Most of what I have read online states, if a function has...

Hey, its bin ages since i did any maths, and gotten a little rusty, am i doing this right when solving these equations? Find a 3/a+1 = 4/a (multiply a+1) 3 = (4a + 4)/a (multiply a) 3a = 4a + 4 (-4)...

Can someone give suggestions for this question? Find a basis of solutions for the following second-order homogeneous linear equation for positive x: x^2y``-xy`+y=0

Ok so here is the problem: You have six steel bearing varying in size and you have their mass and diameter. When you graph the data you see that the mass (in Grams) goes up exponentially as diameter (in cm) goes up. Below is the table of the Mass and Diameters M=.44 D=.4 M=2.04 D=.8...

I am having trouble finding the solution to the homogeneous system of linear equations: 2x-2y+z=0 -2x+y+z=0

I have this intial value problem: y''-4y'-5y=0, y(1)=0, y'(1)=2. My AUX equation is r^2-4r-5=0. I factor and get r=5, r=-1 and my equation becomes y(x)=C1e^(5x)+C2e^(-1x) (C1 and C2 are constants). I took the derivative of y(x) and then tried to use my initial value's to solve for C1 and C2. I...

(a)Show that xy' + 2y = 3x has only one solution defined at x=0. Then Show that the initial value problem for this equation with initial condition y(0)= yo has a unique solution when yo = 0 and no solution when y0=/= 0 . (b) Show that xy'-2y=3x has an infinite number of solutions defined at...

I am trying to solve a linear equation and getting stuck. y' + 2xy = x^2 I am using e^{x^2} as my integrating factor and multiplying that to both sides. Afterwards, I am able to wrap up the LHS as [y e^{x^2}]' and I have [y e^{x^2}]' = x^2 e^{x^2} Now all I need to do is...