# All Questions

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### linear transformations of same form

Let m and n be positive integers and F be a field . Let f1 , . . . , fn be linear functionals on F^n . For any element a in F^n ,define : T(a) = ( f1(a) , . . . , fn(a) ) If T is a linear ...
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### A question about the definition of complete dg Lie algebras in a paper of Lazarev and Markl

In their paper Disconnected Rational Homotopy Theory, Lazarev and Markl give the following definition (page 23): Definition: A complete differential graded Lie algebra is an inverse limit of ...
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### Find the sequence defined by the recurrence equation $x_{n+1} = 4x_n − x_{n−1}, (n ≥ 1)$

Find the sequence defined by the recurrence equation $x_{n+1} = 4x_n − x_{n−1}, (n ≥ 1)$ with $x_0 = 1$ and $x_1=2$. Find an odd prime factor of $x_{2015}$. I've found the characteristic equation to ...
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### Functional Equation: $f(x^2-y^2)=xf(x)-yf(y)$

Let $\mathbb{R}$ be the set of Real numbers. Determine all functions $f:\mathbb{R}\to\mathbb{R}$ such that $$f(x^2-y^2)=xf(x)-yf(y)$$ for all pairs of real numbers $x$ and $y$. This is a problem ...
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### How to find parametric equation between two points in line integral?

[In this example how can we find parametric equations of x and y.] [1] [question]: http://i.stack.imgur.com/lTOnW.png [1] [Solution]: http://i.stack.imgur.com/l8ao7.jpg
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### Why if $\sup f(x) = \inf g(y)$ then there is $z,w$ such that $f(z) - g(w) < \epsilon.$

Let $f : A \to \mathbb{R}$, $A\subset \mathbb{R}^n$, $g: B \subset \mathbb{R}^m \to \mathbb{R}$, $f(A), g(B)$ bounded. Why is true that if $\sup f(x) = \inf g(y)$ then there is $z \in A$ and $w \in B$ ...
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### return coefficients matlab

I'm trying to return coefficients from a 3rd order estimated equation using Matlab R2016a ...
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### “Opposite” point on ellipsis by axis (or vector)

I'm currently working on a little game and am stumped as to how I'd solve this math problem. What I'm trying to do is get the "rotation" needed for B, where B is always opposing A on the Y axis no ...
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### Third Order Differential Equations

I am having trouble solving the third order differential equation $y'''+y'=0$ It was given to me in a quiz (which I got wrong) with boundary conditions $y(0) = 0$ $y'(0)=2$ $y(\pi)=6$ I know that ...
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### Prove $\prod_{k=1}^n(1+a_k)\leq1+2\sum_{k=1}^n a_k$

I want to prove $$\prod_{k=1}^n(1+a_k)\leq1+2\sum_{k=1}^n a_k$$ if $\sum_{k=1}^n a_k\leq1$ and $a_k\in[0,+\infty)$ I have no idea where to start, any advice would be greatly appreciated!
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### Finding basis for column space of matrix

To find a basis for the column space of a matrix one finds the RREF of the matrix. The columns in the RREF are not a basis for the column space, but the same columns in the original matrix are a ...
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### Use past and future data to predict or estimate missing values

I have a huge data set for a single variable $z$ , say WEATHER, not necessarily complete one. That is it has many holes in it(missing data) $z \hspace{3mm} is \hspace{3mm} a \hspace{3mm} 6000\times1$ ...
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### Solving a Three Variable Equation 3;

Today i am facing a problem which involves three variable. Question: $$\frac{1}{x}+\frac{2}{y}+\frac{2}{z}=4$$ $$\frac{2}{x}+\frac{1}{y}+\frac{2}{z}=3$$ $$\frac{6}{x}+\frac{-4}{y}+\frac{1}{z}=0$$ I ...
### $2^{49}$ ways to choose a set of integers $\leq 50$ with odd sum
Problem: Show that the number of ways one can choose a set of distinct positive integers, each smaller than or equal to $50$, such that their sum is odd, is $2^{49}$. My attempt: Suppose set ...
According to (hope my calculation below is correct) https://en.wikipedia.org/wiki/Quadratic_function a bivariate quadratic function is a second-degree polynomial of the form  ...