Find the determinant of a $4 \times 4$ matrix using row reduction

The original matrix is: \begin{bmatrix} 1 &2 &0 &1 \\ 3 &3 &3 &9 \\ 1 & 4 & 1 &4 \\ 1 & 1 & 2 &0 \end{bmat...

Problem in the "proof" of Eisenstein's criterion on irreducibility.

I have a problem about a line inside the following proof which is actually from the book Abstract Algebra by Dummit & Foote Proposition (Eisenstein�...

A way to test whether a function is odd/even using calculator

Could you show me an easy and fast way to test whether a function is odd or even using the calculator ? I've only came across the graphing way and an...

How to work out the test statistic of a coin flip?

Given a fair coin, what’s the p value of getting at least 14/20 heads. Am I correct in assuming Null hypothesis — P(heads)=0.5 Alternate hypothesis — P(he...

Prove the LCM (Least Common Multiple).

$\newcommand{\lcm}{\operatorname{lcm}}$ Let $m,n$ $\in$ $\Bbb N$. The least common multiple ($\lcm$) of $m,n$ is the smallest natural number $x$, such tha...

Finding probability $P(X

Rule for multiplying rational numbers (follow-up)

I was thinking about the rule where $\space\frac{a}{b}\cdot \frac{c}{d}=\frac{ac}{bd}$ and why it worked, and I found this question: Rule for multiplying ...

Equation of a line passing through the origin

I have the question "Write down the equation of the line passing through the origin and perpendicular to y = 2X + 3". I know that the equation of a line i...

Gaussian Poincare inequality for Normal Random Variables that are not Standard

Let $X$ be a standard normal random variable. Then, for any differentiable f:R→R such that $\mathbb{E}f(X)^2<∞$ the Gaussian Poincare inequality states...

Matrix to the power t.

Compute the matrix $A^t$ for the following cases: $A_1=\begin{bmatrix}0&0\\0&1\end{bmatrix}, \quad A_2=\begin{bmatrix}-1&0\\0&-2 \end{bmat...