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

    Yes. My Monday lecture did not spoke about bases or dimensions. But we did take about linear combination and linearly independent sets as well as a vector space.
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    One set v is a linear combination of u. Prove u is linearly dependent

    How can I do it without any theorems about bases and dimensions of linear spaces?
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    One set v is a linear combination of u. Prove u is linearly dependent

    What is the other route? I might easier to understand.
  4. C

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

    I am an typo. I gave the wrong inequality symbol. Sorry
  5. C

    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

    I checked with my calculator. My sequence is the same as the matrix given.
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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)

    Polynomial interpolation would works well in this data. But pade approximate would better because the error would be smaller. The best situation is having a defined function that does not happen in many cases in application problems. It is usual given by data points.
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    I Finding a Rational Function with data (Pade approximation)

    Because I am learning about pade approximation and I am presenting this method to my colleagues, I need to know where to start. I understand that I can do the polynomial interpolation.
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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

    no. I think that your condition is not possible I can pick a N bigger than R...
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    Showing that S is unbounded by contradiction

    I talked to my professor about this question. He recommended me to do proof by contradiction on this question. I need to practice this method. It is good practice for me to do so. I know that the sequence needs move away from the closed ball...
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    Showing that S is unbounded by contradiction

    I am confused....are we still using proof by contradiction?
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    Showing that S is unbounded by contradiction

    A set S is bounded if there is a closed ball B(r,p)=\{(x,y)\in \mathbb{R}^2: |(x,y)-p|\le R}\ such that B(r,p) is a subset of S. Based by the assumption, I am "given a R" but i can't know the "R".
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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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    A Prime Factorization Theorem and Number Systems

    Another one is the a 2×2 matrix that has all the same integer entries. Will not have a fundamental theorem of arithmetic, I think the only unique factorization is a matrix of -1 or 1. There is a paper in the MAA Journal math monthly for more information about matrix number theory.
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    Proving the preimage of a singleton under f is a singleton for all y

    The professor was typing quickly and forget then statement. If #f^{-1}({y})# is a singleton for all #y \in Y#, then #f# is bijection.
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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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    Prove rare trig identity

    My question was meant for the person who posted the homework question, sorry for the confusion.
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    Prove rare trig identity

    do you know sum or difference identities for tangent ?
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    Using a Problem Solving Technique for a simple word problem

    I exclude geometry because it is a proof writing course before calculus. I agree with your assessment.
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    Using a Problem Solving Technique for a simple word problem

    Thank you for your explanation of why I was wrong with my reasoning.
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    Using a Problem Solving Technique for a simple word problem

    I got a negative number as my solution. The back of the book, its positive.
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    Using a Problem Solving Technique for a simple word problem

    I think this was an example for me and the other tutors to follow these steps in order to help the intermediate algebra students when I was undergraduate school. I agree with you that this is a common algebra skills. I also struggles with word problems. And I want to remedy that struggle.
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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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