updates
Does cross product have an identity?
Does cross product have an identity? I.e. Does there exist some $\vec{id}\in \mathbb{R}^3$ such that $$\vec{id} \times \vec{v} = \vec{v}\times \vec{id} = ...
Apr 20, 2026
Archive: Updates
updates
How to obtain an approximate expression for $\sqrt{\varepsilon}$ where $\varepsilon \ll 1$?
Is there a way to obtain an approximate expression for the square root $\sqrt{\varepsilon}$ of a small number $\varepsilon \ll 1$? To be more precise, I w...
Apr 20, 2026
updates
If $A^2$ is invertible, then $A$ is also invertible?
True or False: If $A^2$ is invertible, then $A$ is also invertible. ($A$ is a matrix here.) The answer is true. I was trying to come up with an example th...
Apr 20, 2026
updates
What is the Jacobi amplitude?
This has been bothering me for a while now, and it keeps giving me trouble - how does one explain the Jacobi amplitude, and how does one calculate it? I&#...
Apr 20, 2026
updates
Why are the standard form of non-homogeneous linear DVQ and the general solution equations true?
We are learning about using the Wronskian matrix to determine linear independence of a set of solutions to find the general solution of an equation: $$y =...
Apr 20, 2026
![Does a matrix need to be square for linear independence? [closed]](https://news.conceivablytech.com/uploads/does-a-matrix-need-to-be-square-for-linear-independence-closed_720.jpg)
updates
Does a matrix need to be square for linear independence? [closed]
Does a matrix need to be a square ($3\times 3$, $4\times 4$, etc.) to be linearly Independent? Or do the columns just have to be $\geq$ the rows?
Apr 20, 2026
updates
Which expression is equivalent to $\left(\frac{2}{3}-\frac{2}{x}\right) \div \frac{x-3}{x}$? (from Khan academy)
I've been trying to understand this problem for hours but not getting it. HELP!!! The correct answer is $\frac{2}{3}$, but I don't know why this...
Apr 20, 2026
updates
Finding the angular speed of a rolling press?
A printing press has a roller 23 inches in diameter. A point on the rollers surface moves at a speed of 90 feet per second. What is the rollers angular sp...
Apr 20, 2026
updates
Most basic equation: Heart rate is in units of bpm. What are the units of "b"?
This is the most simple question in the world, but it is surprisingly difficult to explain to a student. The heart rate is measured in bpm, beats per minu...
Apr 19, 2026
updates
Finding squared norm of vector
Suppose you have a $2\times 1$ column vector $x=[7,2]^{T}$. How would you find $||x||^{2}$? Would it be $7^{2} + 2^{2}$? Is this equivalent to the distanc...
Apr 19, 2026
