In general, what is the most straightforward way to find the span of a set of vectors? I'm trying to find the span of these three vectors: $$\{[1, 3,...

I used the following matlab code to solve a system of algebraic equations, but I got no answer. clear; clc; close all; syms x y z u eqns = [2x + 1 == 2ux,...

The axioms that define an inner product in a vector space $V$ are Positivity $\langle v,v\rangle\ge 0$ for all $v\in V$ Definiteness $\langle v,v\rangle=0...

If the position vector of a particle in the cylindrical coordinates is $\mathbf{r}(t) = r\hat{\mathbf{e_r}}+z\hat{\mathbf{e_z}}$ derive the expression for...

Let $b \in \mathbb{R}$ and $X \sim \mathcal{N}(\mu,\sigma^2)$ be a Gaussian distribution with mean $\mu$ and variance $\sigma^2$. I am trying to evaluate ...

I'm reading through James Munkres' book, Topology, and the theorem about the image of a connected space under mapping being connected. To paraph...

Everywhere I read online people use trig substitution to solve it, but I want to understand why in the world this isn't the right way of doing it? $$...

I am not sure whether this question is even well-posed. But today I learnt that $e^Df(x) = f(x+1)$ where $D$ is differential operator and $$e^D \triangleq...

Today we learned about Pythagoras' theorem. Sadly, I can't understand the logic behind it. $A^{2} + B^{2} = C^{2}$ $C^{2} = (5 \text{ cm})^2 + (...

I'm reading a textbook where the Spectral Theorem for symmetric matrices is proven. I understand almost everything about the proof except for one thi...