Show that the eigenvalues of a unitary matrix have modulus $1$. I know that a unitary matrix can be defined as a square complex matrix $A$, such that $$AA...

I understand how combinations and permutations work (without replacement). I also see why a permutation of $n$ elements ordered $k$ at a time (with replac...

We have two bags, Bag A has 40 red balls and 15 blue balls, Bag B has 40 blue balls and 10 red balls. One of these bags is selected at random and from it ...

I used MATLAB eig() to find eigenvectors and eigenvalues of a complex symmetric matrix. I searched through MATLAB online documentation to find a link to s...

I am studying algorithms and i saw a definition like the following: Given $3$ points $p_1 = (x_1, y_1)$, $p_2 = (x_2, y_2)$ and $p_3 = (x_3, y_3)$, $p_3$ ...

$\dfrac 00=x$ $0x=0$ $x$ can be any value, therefore $\dfrac 00$ can be any value, and is indeterminate. $\dfrac 10=x$ $0x=1$ There is no such $x$ that sa...

Solve the partial differential equation $$u_t=3u_{xx}, u(0,t)=0, u(x,0)=\cos{x}\sin{5x}$$ Attempt: Using separation of variables, let $u(x,t)=f(x)g(t)$, s...

With the help of Chinese remainder theorem show that $ x^{144} \equiv 1 \pmod{323}$ for all $x$ relatively prime to 323. The problem with me is that I use...

I'm given this expression $$ (x+y'+z')(x'+z') $$ the $'$ meaning not. I have to simplify this to 3 literals and show my answ...

So I have this question here which says: $a)$ Find the standard matrix of the linear operator $T:R^2\rightarrow R^2$ given by the orthogonal projection on...