Solve the following system of linear equations: x + y + z = 4 x + y + z = 4 2x + 2y + 2z = 8 I'd like some help understanding how to go about solving...

$$a_{0} = 0$$ $$a_{1} = 1$$ $$a_{n} = a_{n-1} - a_{n-2}$$ I have to find the solution of this equation ($a_{n} = ...$, non-recursive, you know what I mean...

Given a set $A = \{1,2,...,n\}$, the number of subsets of this set can be given by the cardinality of the powerset of A: $$|\mathscr P(A)| = 2^n$$ This is...

CONTEXT: Uni question made up by lecturer So I have found the Maclaurin series of $f(x)=x^2e^{x^2}$ to be $\sum_{n=0}^\infty \frac{x^{2n+2}}{n!}$ which ca...

My attempt so far: $$ \tan x = \sqrt3 $$ $$ \frac{\sin x}{\cos x}= \sqrt3 $$ Then I look at the unit circle to find possible solutions. I find two solutio...

While reading a chapter on diagonalizable matrices, I found myself wondering: Can a matrix $A \in \mathbb R^{n \times n}$ be invertible but not diagonaliz...

Please forgive my lack of knowledge, which i think it's one of those basic formula related to Trigonometry. Let's look at visual example: https:...

I cannot understand why $\mathbb{R}^2$ is not a subspace of $\mathbb{R}^3$. My reasoning is as follows: Choose any elements $v_1$ and $v_2$ from $\mathbb{...

There are theories that prove the existence and non-existence of Souslin trees [exist if $V=L$, don't exist if $\mathsf{MA}(\aleph_1)$] and Kurepa tr...

Theorem: Let $Y=X\beta+\varepsilon$ where $$Y\in\mathcal M_{n\times 1}(\mathbb R),$$ $$X\in \mathcal M_{n\times p}(\mathbb R),$$ $$\beta\in\mathcal M_{n\t...