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excel- function with multiple variables
So I'm not good with excel (computers in general) and can do some things but this one is out of my league. This is the problem: The cost of a used ca...
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Recursively constructed set definition
Let $\Sigma$ be some finite set of elements. A function $f$ is a mapping: $f: \Sigma\rightarrow\Sigma$. Let also define that elements of $\Sigma$ has some...
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I need an intuitive explanation of eigenvalues and eigenvectors
Been browsing around here for quite a while, and finally took the plunge and signed up. I've started my mathematics major, and am taking a course in ...
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What does "symmetric about the origin" mean?
What does it mean when a graph or a point on the Cartesian plane is symmetric about the origin or with respect to the origin?
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What exactly is an $R$-algebra?
I've looked up numerous definitions, and all of them talk of a new operator that is added to the $R$-module that is the $R$-algebra. One definition s...
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About how to understand the third isomorphism theorem
What is a good way to understand the intuition behind the third isomorphism theorem? Is it something looking like zooming out of the group structure?(i.e....
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Rational Zero Test of Polynomials
Say I'm trying to find the factors of $r^3 - 3r^2 + 3r - 4 = 0$ I thought I could do the rational zero test by finding the factors of p and q and the...
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Using elementary row or column operations to compute a determinant
How do you use elementary row or column operations to find the determinant of the following matrix? $$\begin{bmatrix} 1 & 7 & -3\\ 1 &3 & ...
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Gauss's Lemma Proof
Theorem 2.39 (Gauss’s Lemma). A polynomial $f ∈ \mathbb{Z}[x] ⊆ \mathbb{Q}[x]$ of the form $$f(x) = x^n + a_{n−1}x+^{n−1}+ ...+ a_1x + a_0$$ is irreducibl...
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Proof square root of 4 is not irrational.
I was recently working on a question essentially worded in the following way: Where does a proof of $\sqrt{4}$ being irrational fall apart when we try to ...
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