Matrices - Find x, y and z
I have two matrices $A$ and $B$ and I'm trying to figure out what $x$, $y$, and $z$ are. $$\begin{bmatrix}x+2y&x\\-x+y&2x-y\end{bmatrix} = \b...
Apr 19, 2026 1 VIEWS
Topic: General
5104 Articles 
Understanding the Co-finite Topology on R
I'm looking to gain a better understanding of how the cofinite topology applies to R. I know the definition for this topology but I'm specifical...
Apr 19, 2026 2 VIEWS
Prove that for a real matrix $A$, $\ker(A) = \ker(A^TA)$
So clearly the kernel of $A$ is contained within the kernel of $A^TA$, since $$A^T(A\vec{x}) = \vec{0} \Rightarrow A^T(\vec{0}) = \vec{0}$$. Now we need t...
Apr 19, 2026 1 VIEWS
How to prove Bonferroni inequalities?
Define $$S_1 = \sum_{i=1}^n P(A_i)$$ and $$S_2 =\sum_{1 \le i < j \le n}^n P(A_i \cap A_j)$$ as well as $$S_k =\sum_{1 \le i_1 < \cdots < i_k \le...
Apr 19, 2026 1 VIEWS
Is there a formula to calculate the area of a trapezoid knowing the length of all its sides?
If all sides: $a, b, c, d$ are known, is there a formula that can calculate the area of a trapezoid? I know this formula for calculating the area of a tra...
Apr 19, 2026 1 VIEWS
symmetric group of equilateral triangle?
We can represent rotations of a equilateral triangle by matrices . Can we represent flips of a equilateral triangle by matrices ??
Apr 19, 2026 1 VIEWS
Why is displacement ,instead of position, the integral of velocity? [closed]
Why is the term displacement used as being the integral of velocity instead of position. The integral should cancel the derivative.
Apr 19, 2026 1 VIEWS
A math puzzle about slow clock
You have the misfortune to own an unreliable clock. This one loses exactly 20 minutes every hour. It is now showing 4:00am and you know that is was correc...
Apr 19, 2026 2 VIEWS
A bag contains n white and 2 black cards.
A bag contains n white and 2 black cards. Balls are drawn one by one without replacement until a black is drawn. If 0,1,2,3,... white balls are drawn befo...
Apr 19, 2026 2 VIEWS
Prove that every even degree polynomial function has a maximum or minimum in $\mathbb{R}$
Prove that every even degree polynomial function $f$ has maximum or minimum in $\mathbb{R}$. (without direct using of derivative and making $f'$) The...
Apr 19, 2026 1 VIEWS
Proving Big-Omega
I have a tutorial sheet that asks: Prove that $n^2 - 3$ is $\Omega(n^2)$ I understand that: $$f(n) ≥ c g(n) $$ And that to $c > 0$ & $n > n_{0}$...
Apr 19, 2026 1 VIEWS
Meaning of row space
I used to think of the row space of an $m \times n$ matrix $A$ as the column space of $A^T$, and therefore the row vectors are the images of the standard ...
Apr 19, 2026 1 VIEWS