In learning linear algebra, an overarching question that I have is why there is a very specific set of rules that dictates when a system of equations is s...

I am looking at the proof of the following theorem from Apostol's Mathematical Analysis. I am having trouble showing the last part that the author le...

Determine if the following geometric series converges or diverges. If it converges, what is its sum? $$\sum_{i=0}^n \frac{1}{(\sqrt[]{2})^n}$$ So I know t...

I need to calculate how many possible passwords there are if each password is 4 digits long, using the digits 0-9. All digits in the password must be uniq...

I know what "surface area" means for: a 2d shape a cylinder or cone but I don't know what it actually means for a sphere. For a 2d shape Su...

Why do we need QR factorization? Is this used in any particular field?

I am trying to calculate Image to World model for my thesis dealing with road lanes. As a disclaimer I have to say that linear algebra is not my strong su...

When $A \cap B = \emptyset$, $A$ and $B$ are said to be mutually exclusive. Is there a term to describe events that must occur together or sets that perfe...

Let $A,B,C$ be sets. Prove the distributive law $$A \cap\left(B\cup C\right) = \left(A\cap B\right)\cup \left(A\cap C\right)$$ proof First we'll show...

In general when $X$ is an exponential random varaible, the memoryless property is stated as $$\mathbb{P}( X> s+t | X> s ) = \mathbb{P}(X > t).$$ ...