Tagged Questions
1
vote
2answers
18 views
problem with partial fraction decomposition
I want to do partial fraction decomposition on the following rational function:
$$\frac{1}{x^2(1+x^2)^3}$$
So I proceed as follows:
$$\begin{align}
\frac{1}{x^2(1+x^2)^3} &= \frac{A}{x} + ...
0
votes
2answers
32 views
How do I find all real numbers of Y with a nontrivial solution?
My problem is: Find all real values of Y, if any, for which the system has a nontrivial solution.
$$2X_1 + 3X_2 = YX_1$$
$$4X_1 + 3X_2 = YX_2$$
Thank you.
0
votes
1answer
24 views
Find vector and parametric equations of span v
How do I find vector and parametric equations of span $\{v\}$? Need help on steps to take or description.
5
votes
1answer
76 views
Conceptual questions about cross product rules
I am studying cross products and I just cannot get my head around the materials. Can someone explain to me why...
a) The cross product $\vec{a}\times \vec{b}$ is normal to $\vec{a}$ and $\vec{b}$. ...
0
votes
1answer
23 views
Adjust a range of given values. [duplicate]
If I have a number anywhere on the range 140 - 350 and I want to match it to the correlated range "0 - 360" what function can I run it through?
i.e.:140 would go through the function and return 0.350 ...
0
votes
0answers
17 views
Linear Algebra - Aligning two vertices in two meshes
I have two separate objects I have modeled, simple rooms. They need to be fitted together and my method for doing so is to find two vertices that should connect. With raw x, y and z values, I figured ...
-3
votes
1answer
72 views
How to find$ f(x , y)$? [closed]
$f(1 , 1)=1$
$f(2 , 2) = 4$
$f(3 , 4) = 2415$
$f(9 , 12) = 2.5720 \times 10^{46}$
How to construct the function f(x , y) with the above data and find out f(100,500)
Thanks in advance
0
votes
1answer
27 views
How to prove this symmetric polynomial equations?
I got a problem from a friend, which is to prove that $\Sigma _{i=1}^{n}%
\frac{x_{i}^{m}}{\Pi _{j\neq i}(x_{i}-x_{j})}=0$ for m < n-1.
I tried to multiply the left of equation with $\Pi _{1\leq ...
0
votes
0answers
86 views
integral equations - i need help to expand the function
I have the following integral equation to solve:
$$\int_{0}^{2\pi} (\cos^2(x+y)+1/2) \phi (y) dy$$
So, I need to find $\lambda$ where $\lambda$ is the eigenvalues's function. Well, my main goal is ...
0
votes
2answers
35 views
Solving For Variables In Simultaneous Equations
I'm doing some work in linear algebra and these came up and I realized I don't know how to solve them as they have quadratics in them. I'm sure I've done this before but if someone could give me a ...
1
vote
2answers
42 views
How to solve equation like this?
Is there any good method to solve equations like this?
$$
\begin{cases} x^2=y^2\\-6xy+10y^2=16\end{cases}
$$
From the first equation, I see:
$$
1) x=1, y=1
$$
$$
2)x=1, y=-1
$$
$$
3)x=-1, y=1
$$
$$
...
3
votes
3answers
142 views
How to solve these equations with $x^2$, $xy$, and $y^2$?
Is there any good method to solve equations like this?
$$
\begin{cases} 2y-2xy-y^2=0\\2x-x^2-2xy=0\end{cases}
$$
This is what I did:
$$
\begin{cases} y(2-2x-y)=0\\x(2-x-2y)=0\end{cases}
$$
now I see, ...
2
votes
1answer
33 views
Linear independence of $(x\sin x)^{\frac{n-1}{2}}$ and $(x\sin x)^{\frac{n+1}{2}}$
Could you tell me why $(x\sin x)^{\frac{n-1}{2}}$ and $(x\sin x)^{\frac{n+1}{2}}$ are lineraly independent?
I've tried $\alpha(x \sin x)^{\frac{n-1}{2}} + \beta (x\sin x)^{\frac{n+1}{2}} =0$
...
0
votes
2answers
48 views
Non-parallel vectors confusion
I've got a section in my textbook about non-parallel vectors, it says:
For two non-parallel vectors a and b, if $\lambda a + \mu b = \alpha a + \beta b$
then $\lambda = \alpha $ and $\mu = \beta $
...
0
votes
1answer
54 views
Easy way to check for a valid solution in this triple equality?
Let's say I have the following equalities
$a_1x_1 + a_2x_2 + a_3x_3 + a_4x_4 = b_1x_1 + b_2x_2 + b_3x_3 + b_4x_4 = c_1x_1 + c_2x_2 + c_3x_3 + c_4x_4$
Where the $a$'s, $b$'s, and $c$'s are known, ...
0
votes
0answers
64 views
A minimax problem
Let $\omega$ be a non zero real number, $(\lambda_i)_{i = 1}^n$ be a sequence of $n$ real numbers and
$$u_{i}:=1-(1-\lambda_{i})\,\omega.$$
Show that if we pick
...
0
votes
1answer
24 views
Relationship between 2 Dimensional Quadratic systems and roots
Given four points
$(x_1, y_1)
(x_2, y_2)
(x_3, y_3)
(x_4, y_4)$
How does one construct a system of two equations:
$a_1x + a_2x^2 + a_3y + a_4y^2 + a_5xy = c_1$
$b_1x + b_2x^2 + b_3y + b_4y^2 + ...
2
votes
2answers
81 views
Simultaneously solving of equations
I am trying to refresh some math skills and I am struggling over the following problem. I tried to solve it with the help of a number of sources (i.e. http://www.idomaths.com/simeq.php), but I haven't ...
1
vote
0answers
59 views
Solving a system of four equations
If I have a system of four equations and i need to get ratio $E/A$ out of it. How can i do it? $\mathcal K$, $\mathcal L$ and $d$ are conctants, $A$ is independant variable where $B,C$ and $D$ are ...
0
votes
1answer
63 views
Local expansion of a polynomial
I've been staring at this local expansion, from a paper, of a multivariate polynomial but I can't quite understand it. It goes as follows:
$\mathcal{C}$: Field of Complex numbers
Let $x=(x_1, ...
1
vote
0answers
39 views
Finding the zeroes of finite exponential sum
I want to find the zeroes for functions that look like this (an example):
$f(t) = k_1e^\left(a_1t\right)+k_2e^\left(a_2t\right)+k_3e^\left(a_3t\right)$
Where all a are negative real numbers, so this ...
3
votes
3answers
62 views
Solving for three unknowns given three linear equations
Have to admit, I forgot how to do simple 9th grade algebra problems. I need to know how to do this stuff for an exam tomorrow. I am doing recurrences and the only thing I need to do is find $a, b$, ...
2
votes
2answers
90 views
Derivative of $c^TX^TXc$ with respect to $X$
What is the derivative of $c^TX^TXc$ with respect to $X$? Here, all the entries are real and $X$ is a matrix while $c$ is a vector.
I keep getting confused with the left and right multiplication. ...
2
votes
1answer
58 views
Solve a linear equations with 3 unknowns
I have this equations
$$x+3y+6z=3$$
$$x+y+z=-2$$
$$-x+y+4z=7$$
my solution is
$$x=0$$
$$y=-5$$
$$z=3$$
this task is 1 of 3 and there is going to be 1 that can be solved, 1 that will have a ...
0
votes
3answers
42 views
Determining if a Number N can be written as sum of one or more numbers from 1,2…K each used at most once?
How to determine if a natural number N can be written as sum of numbers from 1,2...K such that each number 1,2,3...K is used at most once( ie a number can be used one or 0 times)
Also we need to ...
1
vote
1answer
119 views
What is a relationship between sets and Trinomial Coefficient?
We know that the relationship between set with n Cardinality named A and Binomial Coefficient is all about subsets of the set A with n Cardinality. Binomial Coefficients describes Cardinality of ...
4
votes
4answers
101 views
The matrix I mentioned below is irreducible and primitive or isn't?
$$
\left[
\begin{array}{@{}ccccc@{}}
0.9& 0.1& 0& 0& 0& 0& \\
0& 0.9& 0.1& 0& 0& 0& \\
0& 0& 0.9& 0& 0& 0.1& \\
0& 0& ...
0
votes
0answers
85 views
Formula for distance travelled?
Given the coordinates of source of a missile, and those of the target both of which are on the surface of the Earth $(z=0)$ , I need to determine the total distance that the missile will need to ...
4
votes
3answers
112 views
Order of calculation in all math equations
I already asked a question (Order of operations in rotation matrix notation.) about the order in which a particular equation is "processed" and now I need to generalise that and learn the rules of ...
4
votes
3answers
264 views
There isn't a product operation that is commmutative on $ \mathbb{R}^{n} $ that satisfies all the field axioms for $ n \geq 3 $.
This proof is broken down into simple easy algebra and vector questions. I would like to discuss different answers and approaches.
Please see pg 162-163 on books.google.ca/books?isbn=0387290524
...
0
votes
1answer
49 views
Simplifying equation from an aggregate one
I have got the 4th order coefficient of $\epsilon$ from the equation (9) from the paper.
I got :
$$\phi_4+ \ddot \phi_4+\omega_2 \ddot \phi_2 - \Delta \phi_2+g_2 \phi_2^2+2 \phi_1 \phi_3+ 3g_3 ...
0
votes
1answer
27 views
Proportionality and Linearity
I have a very basic question that a friend and I are disagreeing on.
Does (direct) proportionality between two terms a and b imply linearity between the two terms?
0
votes
1answer
59 views
Overdetermined system of equations
$x_{1}=u+v$
$x_{2} = \zeta u + \zeta^{2} v$
$x_{3} = \zeta^{2} u + \zeta v$
where $\zeta = -\frac{1}{2} + i \frac{\sqrt{3}}{2}$
Since $\zeta$ is a third root of unity, $\zeta^{3} =1 $.
Also, ...
1
vote
2answers
69 views
Problem with graphing linear equations
Well, I can understand how to graph basic liner equations, for example:
$$y=2x-4$$
The y-intercept would be -4 and the slope would be 2. The coordinates could then be (0,-4)(1, -2)
However, how ...
1
vote
1answer
32 views
Calculate how long it take to reach a goal
Given a growth rate for a period and a goal. How can I calculate how many periods that it will take to reach that goal.
Example:
An investment currently valued at $400 grows at 30% per week.
...
1
vote
1answer
32 views
how to find cosinus betwen two vector?
i have task in linear-algebra.
Condition:
we have triangle angles
A(-4,2);
B(-1,6);
C(8,-3);
How to find cosinus between BA and BC vectors?
please help :( what ...
1
vote
3answers
88 views
Solving complicated fraction for X
I realize this rather rudimentary but it has been over a decade since my algebra classes and now I have problem that I can't figure out. I would like someone to walk me through the steps in solving ...
2
votes
1answer
52 views
Linear system with probabilities (algebra)
I have a small problem that delays my project , it seems I am stuck here loads of time. It is probably very easy but I cant see it right now , I am very anxious about this, please take a look:
...
2
votes
2answers
195 views
finding the intersection of two line segments in 2d (with potential degeneracies)
I am trying to write an algorithm that finds the intersection of two line segments in the plane. The line segments are given as pairs of points, which I'm writing as $C_1$ and $C_2$, where $C_1 = ...
0
votes
1answer
84 views
How to Simplify this to the given answer? (matrix equation, trig functions)
Can someone help me to simplify
$$\Bigg( \begin{matrix} 5\cos t &5\sin t \\2\cos t+\sin t & 2\sin t-\cos t\end{matrix} \Bigg)
\Bigg( \begin{matrix} u_1 \\u_2\end{matrix} \Bigg)
...
1
vote
3answers
76 views
How to solve this equation in two variables
My question is:
How to solve this equation:
$ax²+by²+cxy=0$
with respect to $x$ and $y$ in the same time. Here $a,b,c$ are real constants.
0
votes
3answers
96 views
System of equations homework
Given the sytem of equation $y= -x+6$, $y= x/3+c$ with the solution lying in quadrant I, find all possible values of $c$.
0
votes
0answers
34 views
factorisation of polynomial
Given $(z_2-z_3)(1-uz_3)(1-uz_2)-(z_1-z_3)(1-uz_3)(1-uz_1)+(z_1-z_2)(1-uz_2)(1-uz_1)$ , is it possible to factorise to the form $u^2(z_1-z_2)(z_1-z_3)(z_2-z_3)$ ?
Is there any method to expand such ...
0
votes
1answer
66 views
System of linear equations in 8 variables
Although I am currently studying fractional linear transformations in complex analysis, I suddenly had the need to find the "solution" of a system of linear equations but I could not. Unless I have ...
0
votes
1answer
107 views
help me to Solve a trick equation
I am trying to solve a trick question that my teacher gave to me.
This question is related to linear algebra.
I have no idea on where to start with this question. I need some guidance in getting ...
2
votes
1answer
46 views
Finding an equation of solutions of an equation given constraints
$$\left(\frac{ax}{p_1}\right)^2 - \left(\frac{bx}{p_2}\right)^2 = cx \quad\text{and}\quad a\neq p_1, \, \, b \neq p_2$$where $a,b,c$ are nonzero integers, and $p_1$ and $p_2$ are distinct prime ...
1
vote
1answer
70 views
Simplify the expression
The below expression has three summations (sigmas) and $L$ is a real-matrix and symmetric, $X$ is a real matrix with $n$ rows and $X_{p\mathbb{.}},X_{q\mathbb{.}}$ denote the $p$ and $q$ rows of ...
2
votes
2answers
51 views
Problematic complex equation
I got stuck while solving following equation:$$z^6=(1+3i)^{12}$$I think that right side must (at least should) be transformed to form, if $z_{1}=1+3i$ ; $z_1=\sqrt{10}(\cos \theta+i\sin\theta)$ and ...
1
vote
1answer
33 views
Solutions in linear spaces
I came across a task, which is hard to move for myself (just 1st year of math studies). It is:
For what $t\in \mathbb{R}$ set of solutions is a subspace of a $\mathbb{R}^{3}$
$$\\
...
1
vote
3answers
81 views
Find the equation of the plane that contains
Find the equation of the plane that contains,
the lines: $$
\frac{x-2}{2} = \frac{y+4}{3} = \frac{2 - z}{5}
$$
and
$$\begin{align}
x &= 3 + 4t \\
y &= -4 +6t \\
z &= 5 -10t.
\end{align}
...
