How can the eigenvector corresponding to zero eigenvalue be found out? I was trying with the following simple matrix in Matlab: $$A=\left[\begin{array}{cc...

I need to find and prove the possible existence of this limit : The function $f(x)$ is defined as follows: $$f(x) = \left\{ \begin{array}{c} 1, x < -2 ...

If H = [4 4; 4 4] Why is sqrt(H)=[2 2; 2 2] And, (H)^0.5=[1.4142 1.4142; 1.4142 1.4142]

I never knew not having good knowledge of basic maths will be so crippling!! So please help me out this time. I'll be working on my maths from today ...

I recently came across the following expression regarding function composition: \begin{equation} g \circ f : A \rightarrow C :: a \mapsto g(f(a)) \end{equ...

If the circle were centered at the origin, of radius r, then r(cos$\theta$, sin$\theta$) traverses the circle once counterclockwise, for 0 $\le$$\theta$$\...

I am doing differential equation now and I need to convert them into the proper form in order to do my homogeneous differential equation. So now I just fo...

I am proving $(x^n)'=nx^{n-1}$ by the definition of the derivative: \begin{align} (x^n)'&=\lim_{h \to 0} {(x+h)^n-x^n\over h}\\ &=\lim_{...

If $$P(E \cap F) = 0.054$$ $$P(E |F) = 0.12$$ $$P(F | E) = 0.3$$ How Do I find P(F) or P(E)? These are dependent of each other, so I was trying to use the...

1. Suppose that $f(x)$ is (Riemann) integrable on $[a,b]$ and $F^{'}(x)=f(x)$ for all $x\in[a,b]$,then there is a number $\color{red}{\xi\in(a,b)}$ s...