For example,the sum of the digits of the number $139=1+3+9=13$ The smallest $3$ digit number to fulfill this condition is $109$ Essentially,this question ...

This question in my book Let $T:\mathbb{R}^n\to \mathbb{R}^m$ be a linear transformation. Suppose $\{\mathbf{u}, \mathbf{v}\}$ is a linearly independent s...

I am stuck on a problem for my calc 2 course. We are being asked to use Taylor series centered around x=0 (Maclaurin series) to approximate $\sin(x^2)$ an...

I've got two curves: $$(x,y) = (t^2,t+1), \quad t\in\mathbb{R}$$ $$5x^2 + 5xy + 3y^2 -8x -6y + 3 = 0$$ I've found the intersection points: $$(0,...

How can I shift selected column of a matrix (column wise) by matrix multiplication? Let's say I have a matrix like this: $$A=\begin{pmatrix}1 & 0...

Recently I started being very fascinated in logistics, and out of the blue came the question into my head, what is the factorial of the amount of atoms in...

I have a homework question which requires me to find the coefficient of $x^{14}$ in the expression: $\dfrac{5x^2-x^4}{(1-x)^3}$ I have not figured out a w...

The set of $\lambda$ satisfying $$ (A - \lambda I_n)\vec{x} = 0 $$ is called the eigenspace of a matrix $A$ corresponding to $\lambda$. Now I want to writ...

Wikipedia says that a linear transformation is a $(1,1)$ tensor. Is this restricting it to transformations from $V$ to $V$ or is a transformation from $V$...

Suppose I have a few ecuations: $$\cos^2(x) = \sin(x)\cos(x) \Rightarrow cos(x) = sin(x) $$ $$ x^2 + 3x \ge 2x \Rightarrow x(x+3) \ge 2x \Rightarrow x+3 \...