I have to find $\angle MHN$ ($\angle H$ in $\Delta HMN$). It is inside a cube that has side lengths of $12$ cm. $M$ is the midpoint of the diagonal $BD$ and $N$ is the midpoint of edge $GF$. Here's the diagram:
I'm completely lost on how I would find $\angle MHN$ because the triangle is skewed ...0
I have this "generator" function :
$$ g(u,t) = \sum_{k=0}^{n} \sum_{i=0}^{k} \binom{n}{k} \binom{n-k}{i} x^k y ^i e^{\frac{kn}{t}} e^{\frac{un}{t}} = (1-x+y-ye^{\frac{u}{n}} + x e^{\frac{t}{n}})^n$$
And the Bernstein two-variable polynomial (in a triangular domain I think) :
$$B_n(f,(x,y)) = \sum...
3
Rouché–Capelli theorem (Kronecker–Capelli theorem/Rouché–Fontené theorem/Rouché–Frobenius theorem/Frobenius theorem) states that for the non-homogeneous system Ax = b,
$(i)$ $Ax = b$ has a unique solution if and only if $rank[A] = rank[A|b] = n$
$(ii)$ $Ax = b$ is inconsistent (i.e., no solu...
The Rouché–Capelli theorem is a theorem in linear algebra that determines the number of solutions for a system of linear equations, given the rank of its augmented matrix and coefficient matrix. The theorem is variously known as the:
Kronecker–Capelli theorem in Austria, Poland, Romania and Russia;
Rouché–Capelli theorem in Italy;
Rouché–Fontené theorem in France;
Rouché–Frobenius theorem in Spain and many countries in Latin America;
Frobenius theorem in the Czech Republic and in Slovakia.
== Formal statement ==
A system of linear equations with n variables has a solution if and only if the rank...
