Assume the differential equation: $$ x'=\lambda^2-8a\lambda x+2x^2, \quad a\in \mathbb{R}. $$ The critical points are the solutions to the equation: ...

I was asked to find the truth value of the statement: $$ \pi + e \; \text{ is rational or } \pi - e\; \text{ is rational } $$ I am only allowed to use the...

I have a question on determining eigenvalues for a given matrix A: $$ A= \begin{bmatrix} 2 & 1 & 2 \\ 0 & 2 & -1 \\ 0 & 1 & 0 \\ \...

How can I solve the recurrence relation $T(n) = 2T(n/2) + n\log n$? It almost matches the Master Theorem except for the $n\log n$ part.

For any oblique triangle, which may be acute or obtuse, if I know length of two sides, and I know all three angles, how can I determine length of unknown ...

I'm currently taking an intro to linear algebra course. We have reached the section on dot products and I fail to understand the meaning of it. What ...

I have a fair coin. What is the expected number of tosses to get three Heads in a row? I have looked at similar past questions such as Expected Number of ...

For instance, in triangle ABC, how to notate the side AB? Since, as far as I know, to notate the length of the side $AB$, we simply write $AB$ and I presu...

How would I factor to solve for x? $x^5 + 20x^2 + 5=0 $? Do I use synthetic division? Is there a faster/easier way? Do I have to keep plugging in numbers ...

Consider a vector field $\underline{{f}}:\mathbb{R}^3\rightarrow \mathbb{R}^3$. We know that $\underline{\nabla}\cdot\underline{f} = tr(D\underline{f})$, ...