I have the system of equations as follows: $x + y + z =0$ $2x + 3y + 2z = -3$ $-x - 2y -z = 1$ First I added the first and third equation and the result w...

So this is a homework problem. So I'll give what I got. Suppose $A,$ $\ B$ & $X$ are $n$ by $n$ matrices with $A,$ $\ X$ & $A-AX$ invertible....

Show that $Q(x):=200x^3-200x^2+200x+100$ is an irreducible polynomial over the field $\mathbb{Q}$ of rational numbers. I'm trying to use Eisenstein&#...

So I have this equation: $$\frac{2}{3}a^2-\frac{4}{9}a^2 = 8a$$ So this is a really easy problem, I could just multiply $$\frac{2}{3}*\frac{3}{3} = \frac{...

This goes for equipping any set with any topology. Suppose that I want to equip a subset $A \subseteq X$ where $X$ is a topological space, with the subspa...

The problem in question: The population of mosquitoes in a certain area increases at a rate proportional to the current population, and in the absence of ...

Ok, I've been looking at this problem: Let $$f(x,y) = \frac{3}{16}xy^2, \quad 0 \le x \le 2, \quad 0 \le y \le 2$$ be the joint probability density f...

My question is from Arfken & Weber (Ed. 7) 19.2.2: In the first part, the question asks for Fourier series expansion of $\delta(x)$. I have found $$\d...

We know that $(x_n)_{n\in\mathbb{N}} $ defined as $x_n=\sin(n) $ is dense in the interval $[-1,1]$ , can we extend this to prove also $\sin(n^2) $ is dens...

I have found two derivatives of the so-called Riccati-Bessel functions in a textbook $$ (x j_n(x))'=xj_{n-1}(x)-nj_{n}(x)$$ and $$ (x h_n^{(1)}(x))&#...