updates
Proof of the 'Infinite' DeMorgan's Law.
Suppose I wanted to prove $\Big(\bigcup_{n=1}^{\infty} B_n \Big)^c = \Big(\bigcap_{n=1}^{\infty} B_n^c\Big)$. I've written out a proof of this, and w...
Apr 14, 2026
Archive: Updates
updates
Find the growth factor from a point plot
Referring to the graph below, Find the growth factor between the numbers of stick insects in consecutive time intervals of two weeks. Hence find a relatio...
Apr 14, 2026
updates
How to convert the given set of equations into a symmetric form
How do I convert the equations $$\left\{\begin{array}{} 3a +2b+ c & = & 0\\ a+4b+4c & = & 0 \end{array}\right.$$ to the form $$\frac{a}{4}...
Apr 14, 2026
![$AB-BA=A$ implies $A$ is singular and $A$ is nilpotent. [duplicate]](https://news.conceivablytech.com/uploads/ab-ba-a-implies-a-is-singular-and-a-is-nilpotent-duplicate_720.jpg)
updates
$AB-BA=A$ implies $A$ is singular and $A$ is nilpotent. [duplicate]
Let $A$ and $B$ be two real $n\times n$ matrices such that $AB-BA=A$ Prove that $A$ is not invertible and that $A$ is nilpotent. My attempt is the followi...
Apr 14, 2026
updates
How can I prove that F2 is a Field?
I have to prove that the set {1,0} is a field. Do I have to go through every 8 possibilities when I want to show associativity or is there an easier way a...
Apr 14, 2026
updates
What is the proof that First-order logic is complete?
According to Wikipedia, first order logic is complete. What is the proof of this? (Also, in the same paragraph, it says that its undecidable. Couldn'...
Apr 14, 2026
updates
General linear group over integers
I'm trying to get my head around group theory as I've never studied it before. As far as the general linear group, I think I've ascertained...
Apr 14, 2026
updates
Root Locus Diagrams - "Breakaway Point"
Say that we have a root locus diagram with n poles and m zeroes. And we determine that the root locus on the real axis lies between two of these poles and...
Apr 14, 2026
updates
Expected value: Poisson random variable
I have proved that $$E[X^n]=\lambda E[(X+1)^{n-1}]$$ for a Poisson random variable with parameter $\lambda$ where $n$ is a positive integer. Now $E[X+2]=E...
Apr 14, 2026
updates
Using Chain Rule in Matrix Differentiation
I have the following parameters and their respective dimension: $X:2\times 1$, $W_1:7\times2$, $W_2:1\times7$, $B_1: 7\times 1$ and $B_2:1\times1$, with t...
Apr 14, 2026
