I have this linear system: $$ \left\{ \begin{array}{r} x+2y=4 \\ y-z=0 \\ x+2z=4 \end{array} \right. $$ This Linear system can be converted to echelon for...

I've got a function $$g(x,y) = \| f(x,y) \|_2$$ and I want to calculate its derivatives with respect to $x$ and $y$. Using Mathematica, differentiati...

The product has only positive factors so it has zero as lower bound. Also the product is decreasing as all its factors are less than one. In conclusion th...

Consider a linear differential operator $$L=\frac{d^2}{dx^2}.$$ How would one determine that the normalised eigenfunctions of $L$ are $$\phi_n(x)=\sqrt{2}...

I want to calculate the complexity of an algorithm in MATLAB (not the time complexity), however, all the matrices are complex ones. I guess that the compl...

how do you calculate eigenspaces?

As a physics student, I've come across mathematical objects called tensors in several different contexts. Perhaps confusingly, I've also been gi...

Use spherical coordinates to evaluate the triple integral: $$\iiint_{E}{(x^2+y^2+z^2)dV}$$ Where E is the ball: $E=\left\{(x,y,z)\in \mathbb{R}^3 \mid x^2...

Sorry if this is a bit simple compared to everything here, but I can't really seem to find an answer. If I have $$f(x) = \frac{(x-2)(x-4)}{x(x-1)}$$ ...

Let, $$y = mx + c \tag 1$$ is the equation of a straight line. Let, it passes through the point, $$(x_0, y_0)$$. So, from (1) we find, $$c = y_0 + mx_0 \t...