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    One set v is a linear combination of u. Prove u is linearly dependent

    Hi Everybody, I am having some difficulties on the prove this problem. I picked a nice example when I was trying to think about the proof. Let ##s=3## and ##t=2##. Then ##u1=c1v1+c2v2, u2=c3v1+c4v2, u3=c5v1+c6v2##. Then a linear combination of u: ##K1u1+K2u2+K3u3=0##. I grouped both linear...
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    I Factoring Matrices with Elementary Row Operations

    Dear Everybody, I have some trouble with this problem: Finding a sequence of elementary matrix for this matrix A. Let ##A=\begin{bmatrix} 4 & -1 \\ 3& -1\end{bmatrix}##. I first used the ##\frac{1}{4}R1##-> ##R1##. So the ##E_1=\begin{bmatrix} \frac{1}{4} & 0 \\ 0& 1\end{bmatrix}##. So the...
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    I Finding a Rational Function with data (Pade approximation)

    Dear Everybody, I need some help understanding how to use pade approximations with a given data points (See the attachment for the data). Here is the basic derivation of pade approximation read the Derivation of Pade Approximate. I am confused on how to find a f(x) to the data or is there a...
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    Showing that S is unbounded by contradiction

    Dear Everyone, I am attempting a proof of contradiction for this problem. I am stuck on next step. My attempt: Assume that ##S## is bounded. Choose a ##N=\text{greatest integer function of} R+1##... Here is where I am stuck. I want to show that the sequence is moving away from the closed ball...
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    Proving the preimage of a singleton under f is a singleton for all y

    Dear Everyone, I have some trouble how to start the proof of this statement. I need to prove the preimage of the singleton under f is the subset of singleton of x and vice versus. My attempt is this: Given y. So we know that definition of the preimage is when all #x# is in #X# , then #f(x)...
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    Geometry Recommendation for High School Geometry book

    Dear Everyone, So I would like some recommendation for high school geometry books that are affordable and preferably e-books. Why do I need some books on high school geometry? I would like to improve my geometric reasoning. When I took high school geometry a decade and half ago, I was...
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    Using a Problem Solving Technique for a simple word problem

    Summary:: I have a document which was written by previous tutor supervisor/instructor at my undergraduate school. I want to learn how to use this technique for other math/physics subject besides algebra... I will provide an example of how to use this technique. I found an old textbook (College...
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    I Simplifying a nested radical that includes a complex number

    Dear Everyone, This post is not a homework assignment... I want to use the quartic formula. In one step is to solve the resolvent cubic. I know that there is 3 real solutions this particular resolvent cubic. I want to know how Bombelli got his answers before the discovery of the trigonometric...
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    Finding a domain for a function

    I am having some trouble find the domain with this function: ##f(x)=\frac{1}{\sqrt{x^2-4x\cos(\theta)+4}}## and ##\theta\in[0,\pi]##. I know that the denominator needs to be greater than 0. So ##\sqrt{x^2-4x\cos(\theta)+4}>0##. I squared both side of the inequality, ##x^2-4x\cos(\theta)+4>0##...
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    I How to deal with self-doubt in mathematics?

    Dear Everyone, I am wondering how to deal with the self-doubt in proof-writing in general situation like on exam or homework question. Suppose I want to prove Theorem B. I assume the hypothesis. Then I apply the right mathematics definition. I am hesitant on the next step; I have the feeling...
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    B Rigid Transformations and other topics -- help with Learning Geometry?

    Dear Everybody, I am in the process of relearning high school geometry through Khan Academy. I am current an graduated undergraduate student in mathematics. I am doing this because geometry is one of my weakest subject in mathematics. Second reason is that I want to reason out a problem...
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    Stem and Leaf Plot for a Dependent Children-Homework Question

    The exercise is 2.37 in the book, Exploring Statistics: A modern introduction to data analysis and inference by Larry J. Kitchens 2nd editions. The data is the following: 3 2 2 4 1 1 2 3 4 1 2 0 1 2 1 0 4 2 1 0 0 1 3 0 3 2 2 3 0 3 2 5 0 1 2 1 4 3 0 5 2 0 1 1 2 6 1 2 1 5 I know the...
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    I Cauchy Integral Formula with a singularity

    Dear Everyone, I am wondering how to use the integral formula for a holomorphic function at all points except a point that does not exist in function's analyticity. For instance, Let f be defined as $$f(z)=\frac{z}{e^z-i}$$. F is holomorphic everywhere except for $$z_n=i\pi/2+2ni\pi$$ for all...
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