How to find the number of triangles in this figure?
What is the way to find the number of triangles in the figure below? What is the method or logical way to derive this? I am not looking for formulas but p...
Apr 14, 2026 1 VIEWS
Topic: General
5104 Articles 
Coordinate/matrix multiplication
If I multiply a 3d coordinate (padded with a 1 to make it a 4x1 matrix) with a transformation matrix, I get a 1x4 matrix which contains my new (transforme...
Apr 14, 2026 1 VIEWS
How to represent Hadamard product in terms of matrix multiplication?
In the case of two vectors $u, v$ with dimensions $n\times 1$, their Hadamard product can be represented by the following matrix multiplication: $$\mathrm...
Apr 14, 2026 1 VIEWS
Symmetric closure of the reflexive closure of the transitive closure of a relation
Give an example to show that when the symmetric closure of the reflexive closure of the transitive closure of a relation is formed, the result is not nece...
Apr 14, 2026 1 VIEWS
Intuition behind Matrix being invertible iff determinant is non-zero
I have been wondering about this question since I was in school. How can one number tell so much about the whole matrix being invertible or not? I know th...
Apr 14, 2026 1 VIEWS
Questions tagged [expected-value]
Q&A for people studying math at any level and professionals in related fields
Apr 14, 2026 1 VIEWS
Proof $1+2+3+4+\cdots+n = \frac{n\times(n+1)}2$
Apparently $1+2+3+4+\ldots+n = \dfrac{n\times(n+1)}2$. How? What's the proof? Or maybe it is self apparent just looking at the above? PS: This proble...
Apr 14, 2026 1 VIEWS
To Prove the relation between HCF and LCM of three numbers
if $p,q,r$ are three positive integers prove that $$LCM(p,q,r)=\frac{pqr \times HCF(p,q,r)}{HCF(p,q) \times HCF(q,r) \times HCF(r,p)}$$ I tried in this wa...
Apr 13, 2026 1 VIEWS
What are the applications of matrices in real world?
Matrices are considered very important in mathematics. What are some examples of applications of matrices to real world problems that would be understanda...
Apr 13, 2026 1 VIEWS
Reasoning that $ \sin2x=2 \sin x \cos x$
In mathcounts teacher told us to use the formula $ \sin2x=2 \sin x \cos x$. What's the math behind this formula that made it true? Can someone explain?
Apr 13, 2026 1 VIEWS
Does f(3x) = 3f(x)?
Is just listed as a true or false question in my book but I was just thinking when this actually is true or false. For instance if f(x) = cx for some c th...
Apr 13, 2026 1 VIEWS
How to know what the letters mean in math formulas?
For example, see this Wikipedia section on Newton's laws of motion: Newton's Second Law states that an applied force, $\mathbf F$, on an object ...
Apr 13, 2026 1 VIEWS