If I take the basis $(\vec{e_x},\vec{e_y})$ and make a rotation counterclockwise of angle $\theta$, I end up with two new vectors $(\vec{u},\vec{v})$ such...

Describe the relationship between the mathematics of calculating simple interest, and the mathematics behind analyzing arithmetic sequences. How might sim...

Find the basis for the solution space of the system and describe all solutions: $3x_1 - x_2 + x_4 = 0$ $x_1 + x_2 + x_3 + x_4 = 0$ I row reduce the matrix...

I am reading about Solution of the Linear Least Squares Problem. Given the function $$f(\theta) = \frac{1}{2} \lVert y - \Phi \theta \rVert _{2}^{2}$$ To ...

This question is about the right English wording. I give here what I call "counterexamples to Banach fixed-point theorem". What I do, is that I look to wh...

This is not homework; I was just reviewing some old math flash cards and I came across this one I couldn't solve. I'm not interested in the solu...

It is quite possible this question has no answer -- that is, the area cannot be determined from the information given. It's a question I've crea...

For the following question : $f(x) = 2x^2 + 4x $ It asks me to express the following in terms of $x$: $f(-2x)$ What does the question mean by this? Does i...

For constants $a$ and $b$, I know that I can break up $\log(a/b)$ into $\log(a) - \log(b)$. Can I conveniently break up $\log(a - b)$ somehow into several...

Say I pick a number from 1 to 100, and repeat this process 99 more times. What is the probability that no numbers will repeat? Is it correct to say the an...