-1
votes
2answers
51 views

Solving Systems of Equations..!! [on hold]

I actually don't want to solve the systems of equations. I just want to let them equal each other so I can cancel one of them and solve the other one. Example: $E_1\quad x-y=0$ $E_2\quad 2x-2y=0$ ...
2
votes
0answers
28 views

What is the solution to the system $\frac{df_n}{dt} = kf_{n-1}-(k+l)f_n+lf_{n+1}$?

I'm trying to solve the system $$ \begin{matrix} & \frac{df_1}{dt} = kf_1+lf_2 \\ & \vdots \\ & \frac{df_n}{dt} = kf_{n-1}-(k+l)f_n+lf_{n+1} \\ & \vdots \\ & \frac{df_N}{dt} = ...
1
vote
3answers
29 views

number of solution to the given equation.

a,b,c, are all non-negative integers such that a + b + c=100 and 1000a + 300b + 50c = 10000 How many such triplets are possible? i have tried to reduce ...
2
votes
1answer
23 views

Can I convert between a rotation about an axis and a rotation according to two angles (all in 3D) without solving a system of nonlinear equations?

I am writing a program that needs to be able to switch between a rotation described by 2 angles to a rotation described an axis and one angle. I found one way to do this from this question, which ...
0
votes
0answers
14 views

Variable bounds of under-determined linear system

If I have a non-negative, under-determined linear system $\mathbf{Ax}=\mathbf{b}$ $\mathbf{x}\geq\mathbf{0}$ is there a fast way to compute the upper and lower bounds on values of each element of ...
5
votes
4answers
75 views

Solve the System of Equations in Real $x$,$y$ and $z$

Solve for $x$,$y$ and $z$ $\in $ $\mathbb{R}$ if $$\begin{align} x^2+x-1=y \\ y^2+y-1=z\\ z^2+z-1=x \end{align}$$ My Try: if $x=y=z$ then the two triplets $(1,1,1)$ and ...
0
votes
0answers
46 views

Underdetermined system of equations

I am sorry in advance if the question I am going to ask is trivial. I have a problem of underdetermined system of equations (6 unknowns and three equations).All unknowns are between 0 and 1. Are there ...
1
vote
1answer
35 views

Solving an augmented coefficient matrix so there are infinitely solutions

I am trying to figure out this math problem. For what values $a,b$ does the linear system have infinitely many solutions? This is the matrix $$ \left[ \begin{array}{ccc|c} ...
1
vote
2answers
53 views

For which values of $a, b$ does the system of equations NOT have any solutions?

I am trying to solve this math problem: For which values of $a$ and $b$ does the linear system represented by the augmented matrix not have any solution? $$ \left[ \begin{array}{ccc|c} ...
0
votes
1answer
23 views

Cramer's rule and linear dependence/independence test

When you have the system of equations: $$ax + by = e\\cx + dy = f$$ And you do some row operations to eliminate $y$, we get: $$x = \frac{ed-bf}{ad-bc}\tag{1}$$ If we eliminate $x$ we get: $$y = ...
0
votes
0answers
30 views

Converting sums to matrix equations

I am able to transform basic sums to vector/matrix equations. But now I have something like: $$ c_{p,q} = \sum_{n=1}^N \sum_{r=1}^R \sum_{s=1}^S e_n x_{n-q-s,p} \cdot h_{r,s} \cdot g_r \cdot ...
1
vote
1answer
31 views

Find the equation of the plane passing through $P(0,0,1)$ and containing $x=y=z$

Find the equation of the plane passing through $P(0,0,1)$ and containing $x=y=z$ a) y-z=0 b) x-z=0 c) z+x=1 d) x-y=0 My attempt: I considered the point $P(0,0,1)$ for hypothesis and ...
2
votes
2answers
67 views

How to determine the eigenvectors for this matrix

I have the matrix $$\left( \begin{array}{ccc} -\alpha & \beta \\ \beta/K & -\alpha/K \end{array} \right)$$ for which the eigenvalues are ...
0
votes
1answer
29 views

Gaussian elimination easily?

Let $$\left( {\matrix{ 1 & 0 & { - 3} \cr 0 & 2 & {\lambda + 3} \cr 0 & 0 & {5 - {\lambda ^2}/2 - 3\lambda /2} \cr } \left| {\matrix{ { - 3} \cr 2 ...
0
votes
3answers
37 views

Find the solutions set for a linear system

Let $$\left\{ {\matrix{ {a_1x + b_1y + c_1z = d_1} \cr {a_2x + b_2y + c_2z = d_2} \cr {a_3x + b_3y + c_3z = d_3} \cr } } \right.$$ It's given that the unique solution for the system ...
1
vote
4answers
74 views

The relation between $\det(A)$ and $Ax=b$

I wish to understand the the relation between $\det(A)$ and $Ax=b$. Hence, what are the solutions for $Ax=b$ (homogeneous and non-homogeneous) when $\det(A)=0$ and $\det(A)\ne 0$? So, all in all ...
5
votes
1answer
97 views

When is the equation $Ax = b$ solvable in the integers?

Let $A$ be an $m\times n$ matrix with integer entries, $b$ a column-vector with $m$ integer entries. Suppose the equation $Ax = b$ has infinitely many solutions. It is clear that the general ...
1
vote
1answer
23 views

Solving $x' = Ax$ for real $x$ where $A$ is a matrix with complex eigen values

I have the following linear differential equation system: $$x' = A x$$ where $$ A = \left( \begin{array}{ccc} 1 & 0 & 0 \\ 3 & 1 & -2 \\ 2 & 2 & 1 \end{array} \right) $$ I ...
0
votes
2answers
55 views

Find conditions on a, b, c, and d for which the following system has solutions:

Find conditions on $a$, $b$, $c$, and $d$ for which the following system has solutions: $$2x+4y+z+3w=a $$ $$-3x+y+2z-2w=b $$ $$12x+5y-4z+12w=c $$ $$13x+10y-z+13w=d$$ I got the system down to: ...
0
votes
1answer
21 views

Solutions of a system of linear equations with a parameter

I've come across a linear algebra problem that I'm not sure how to solve. It's a generic problem - I have to find the solutions of a system of equations dependent on a parameter. So, my first though ...
0
votes
0answers
17 views

What is a minimal equation system?

In the optimization seminar I have to study the quadratic linear ordering problem. And there is one lemma saying some equations form a 'minimal equation system' of a polytope. Does anybody know, what ...
0
votes
2answers
33 views

Make this system of 3 equations solvable for $x$, $y$ and $z$

I have the system of these three equations: $$ax = y+z$$ $$by = x+z$$ $$cz = x+y$$ How do I find all $a$, $b$ and $c$ for which the system has real, positive solutions for $x$, $y$ and $z$? As a ...
0
votes
1answer
71 views

Solving a system of equations using Newton's method

The following paper http://benisrael.net/Newton-MP.pdf provides a way to solve a system of equations using Newton's method. (The theorem begins at the end of page 2) I can't understand the ...
1
vote
1answer
50 views

An example on my book that asks for the basis of an eigenspace

Let $$ A = \begin{bmatrix}4&-1&6\\2&1&6\\2&-1&7\end{bmatrix}$$ An eigenvalue of A is 2. Find a basis for the corresponding eigenspace. Solution: Form $$A-2I = ...
0
votes
3answers
47 views

How does a row of zeros make a free variable in linear systems of equations?

I don't understand how a row of zeros gives a free variable when solving systems of linear equations. Here's an example matrix and let us say that we're trying to solve Ax=0: $$\left[ ...
1
vote
0answers
19 views

How do I generate some sample solutions for an underdetermined system?

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 ...
2
votes
0answers
43 views

How to solve this system of inhomogeneous differential equations

In some past exam papers for the Maths course that I attend,I found this example and I would really appreciate if someone looked at my solution. It goes like this: Find general solution to $$ y_1' = ...
0
votes
1answer
45 views

Solving system of 3 equations

How do I solve the following system? $$ \left\{ \begin{array}{} x_o = 4 - x_r \\ x_r = -2 - x_s \\ x_s = 2 - x_r \end{array} \right. $$ All the techniques i've found for solving 3-equation ...
2
votes
2answers
62 views

Solve a system of linear equations

$\newcommand{\Sp}{\phantom{0}}$There is a system of linear equations: \begin{alignat*}{4} &x - &&y - 2&&z = &&1, \\ 2&x + 3&&y - &&z =-&&2. ...
0
votes
2answers
33 views

Method for Finding Matrix-Inverse Through Gauss-Jordan?

When trying to find the inverse of the n$\times$n matrix $A$, one way of going about it is by solving $AX=I$, wherein $I$ is the n$\times$n identity matrix, and $X$ is some n$\times$n matrix which is ...
0
votes
0answers
35 views

Solving a set of equations

I have a set of n equations of the form of $Z_i((a-x_i)^2 + (b-y_i)^2 + c^2)$, i varies from 1 to n and $Z_i$, $x_i$, $y_i$ are knowns and $a,b,c$ are unknown. They are all equal to each other ...
2
votes
2answers
76 views

How to solve this system of equations that appears in a ODE exercise?

I am trying to solve this equation, we know $A, B, Q,\phi\in\mathbb{R}$. \begin{eqnarray} T''(x) &=& \phi (T(x)-Q) \\ T(0)&=& A\\ T(b)&=&B \end{eqnarray} So the ...
1
vote
2answers
33 views

How to solve this equation with three variables with an unknown parameter using Gaussian elimination?

If I've got three equations: $$\begin{array}{ccccccc} x & + & y & + & z & = 3 \\ 2x & + & ay & - & 2z & = 4 \\ x & + & 2y & - & az & = 1 ...
1
vote
1answer
38 views

how to find matrix A from complete solution to Ax=b

I am trying to solve a problem. I was stuck.Any help is appreciated. The complete solution to $Ax=\left[\begin{array}[c]{rr}1 \\3 \end{array}\right]$ is $ x= ...
0
votes
2answers
49 views

Solve Linear Sytem of Equation for $u,v,w$

I need to solve this sytem for $u,v,w$. I´ve tried basic algebra, but my answer does not mach the one from the book.
2
votes
1answer
54 views

Is it possible for a system of equations to have a non-zero determinant and no solution at the same time?

I am quite confused by the solution I was given for the following problems: a) Solve the following system of equations using Gauss elimination only: $2x - y = 5$ $-x + 2y = -4$ $3x - y = -1$ b) ...
1
vote
1answer
39 views

PRobability Markov chain, system of equations

I'm looking for techniques or tricks to solve a system of linear equations you get where you want to find the limiting probabilities. The system is this: $\pi_0 = 0.7\pi_0 + 0.2\pi_1 + 0.1\pi_2$ ( ...
0
votes
1answer
47 views

System of equations with a unique solution, no solution or an infinite number of solutions

I was doing a past OCR Further Pure 1 Paper from January 2011, but came across the following question that I could not solve, even with the help of the mark scheme: Determine whether the ...
0
votes
0answers
31 views

a system of linear equations $x-y+z=0$

Yall are probably gonna think me a noob. But I am working on this eigenvector problem and I reduced the matrix to $x-y+z=0$ . How do I describe this solution set. I know how to do it if it's just ...
0
votes
0answers
10 views

Finding an isometry in high dimension

Given two points $x,y \in \mathbb{R}^D$, I am looking for the isometry $A\in \mathbb{R}^{D\times D}$ that maps $x$ to $y$: $Ax=y$ I want to determine the $D^2$ parameters constituting $A$. When is ...
0
votes
1answer
37 views

Finding equations when given new center of a circle

$y = −x + \sqrt{2}$, $y = −x − \sqrt{2}$, $y = x + \sqrt{2}$, and $y = x − \sqrt{2}$. These equations determine lines, which in turn bound a diamond shaped region in the plane. Construct a diamond ...
1
vote
3answers
72 views

How do we know that if $Ax = b$ has a unique solution, $A$ is invertible?

We are of course assuming $A$ is an $n\times n$ matrix. I know there's a proof of it going the other way (invertibility implies a unique solution), but I'm trying to work out a proof going this way. ...
1
vote
2answers
34 views

Systems of equations by substitution help

I'm trying to solve a systems of equations problem but I can't seem to see what I'm doing wrong... As far as I can tell the way to solve a system of equations by substitution involves the following ...
0
votes
2answers
35 views

Solvability of this linear equation system and finding particular solution/

I have been given a task, that involves determining if this lin.eq.system $$ x_1+2x_2-3x_3+10x_4-x_5=7\\x_1-2x_2+3x_3-10x_4+x_5=9\\x_1+6x_2-9x_3+30x_4-3x_5=5 $$ has a solution by using what our ...
2
votes
3answers
54 views

Does adding two linear equations will result in a line which will pass through an intersection of the linear equations?

I was wondering why it is almost impossible to find a geometrical explanation of why adding two linear equations helps us to find a solution of a system of linear equations? Am I right that adding two ...
0
votes
4answers
86 views

What am I doing wrong here?

Consider this system of equations: $$ \begin{cases} x+y=6\\x-y=5\\2x+3y=7 \end{cases} $$ This is an overdetermined system and doesn't have a solution (the 3 lines don't intersect). But by adding 2nd ...
0
votes
0answers
29 views

determine in what grid rhombus is a point

i have a rhombus ( i.e. diamond) grid determined by these equations ...
2
votes
3answers
28 views

Solve the following system of linear equations for any values of real parameter $a$…

For any values of parameter $a$ solve the following system of linear equations: $$\begin{cases} x+y+2z=1 \\ 2x+ay-z=4 \\ 3x+y+3z=1 \end{cases} $$ Calculating the value of determinant I found out, ...
0
votes
1answer
73 views

Linear systems. Please help me solve this

Please help me solve this. Consider for every real number $a$ the linear system of equations: $$ \begin{align} x +( a + 1 )y + a^2 z &= a^3 \\ (1-a)x +( 1 - 2a )y &= a^3 \\ x +( a ...
0
votes
2answers
50 views

How to solve this type of problems?

I'm struggling in solving this equation and tried to use the elimination method but did not work with me. Can anyone please show me how it can be solved? $$ -555=0.862X+0.138Y-0.345Z, \\ ...