I cant really find a proper definition for this. If two sets are congruent, then what does that mean. I heard that it can be defined in terms of isometrie...

My teacher ask a question to me. Question is: Determine in how many ways can be rearranged the letters of the word ECEHUCDE so that the consonants and vow...

I'm trying to find the Covariance of $X$ and $Y$. I see that the $Cov(X,Y) = E[XY] - E[X]E[Y]$. I know how to find the expectation of single variable...

Let $E$ be an empty set. Then, $\sup(E) = -\infty$ and $\inf(E)=+\infty$. I thought it is only meaningful to talk about $\inf(E)$ and $\sup(E)$ if $E$ is ...

given : $x^2+6x+2y-8=0$ at $x = 3$ $y = \frac{17}{2}$ $y' = 0 = m_T$ I was able to find the equation of the tangent line which is $y=\frac{17}{2}$ by...

I came across the following problem: Show that if $x$ and $y$ are real numbers with $x <y$, then there exists an irrational number $t$ such that $x <...

I'm dealing with the $3 \times 3$ matrix: $$ \begin{pmatrix} 3 & 4 & 0 \\ -4 & 3 & 0 \\ 0 & 0 & 1 \end{pmatrix}. $$ I have th...

How can I prove that: A and ( not A or B) is equivalent to A and B It is easy to show with a truth table how can I do only using the properties of the log...

Show that canonical projection $\pi:\mathbb{R}^{n+1}\setminus \{0\}\rightarrow \mathbb{RP}^{n}$ is open. I tried to prove it, but I have a hard time pulli...

For the following problem: using Gauss-Seidel iteration method using partial pivoting find the solution of following system up to 5 iterations with initia...