How does one get the inverse of 7 modulo 11? I know the answer is supposed to be 8, but have no idea how to reach or calculate that figure. Likewise, I ha...

I am trying to understand what "Equating the Coefficients " means I am given the following: $$ t_1 \left(t_2+\frac{1}{x+1}\right)+\frac{2 t_2}{x}=t_1^2 b_...

Cayley Hamilton Theorem states that if $A$ is an $n \times n$ matrix over the field $F$ then $p(A) = 0$. We note that $p(\lambda) = \det(\lambda I - A)$. ...

In the given figure, $PQRS$ is a parallelogram. $PQ$ is produced to $L$ so that $QL=PQ$. The line $SL$ cuts $QR$ at $O$. Prove that: $\triangle PQS=2\tria...

For the limit $$\lim_{x\to 5}\sqrt{x-1}=2$$ find a $\delta>0$ that works for $\epsilon=1$. In another words, find a $\delta>0$ such that for all $x$...

I'm currently working through a proof of the divergence theorem for simple volumes. I've found some steps of the proof not formal enough, and I ...

How to find the square root of an irrational expression, to simplify that root. e.g.: $$ \sqrt{ 8 - 4\sqrt{3} } = \sqrt{6} - \sqrt{2} $$ Easy to verify: \...

The solution set of the equation $$\cos^2 x + \sin x +1 = 0$$ is? I haven't studied trigonometry, I'm kinda lost on this issue ...

Given the function $f : \mathbb{R}^3 \to \mathbb{R}$ defined by $f(x,\,y,\,z) = (x - 1)^4 - (x - y)^4 - (y - z)^4$ it presents a unique critical point of ...

I just learned about Laplace Expansion for determinant calculation in high-school, they taught me how to calculate minors cofactors and everything but the...