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(a)Find the Determinant of \begin{equation} A=\left[\begin{array}{ccc} 0 & 1+i & 1+2i\\ 1-i & 0 & 2-3i\\1-2i & 2+3i & 0\end{array}\right] \…

Obtain the following matrices and describe them (a)$A=[a_{ij}]$ is a $3\times3$ matrix such that $a_{ij}=a$ if $i\leq{j}$ and zero otherwise. (b)$B=[b{ij}]$ is …

Question : prove or disprove that $(A+B)^2=A^2+2AB+B^2$ if $A=[a_{ij}]$ is a matrix of $3\times3$ such that $a_{ij}=1$ if i+j is even and it zero otherwise and $B=[b…

The Borel-Cantelli Lemma asserts that let (X,Σ,μ) be a measure Space, if (An) is a sequence of measurable sets such that

Let f and g be differentiable at a point x0εDom(f)nDom(g)  show that (1)       (f+g)'(x0)=f'(x0)+g'(x0) (2)       (fg)'(x0)=f'(x0)g(x0)+f(x0)g…

Prove Or Disprove That a Continous Function is Uniformly Continous.                      PROOF To proof that a Continous Function is Uniformly Continous is simple …

Theorem: Let f(x)→L, g(x)→L' then x→a and cεR  then we have (a) f(x)+g(x)→L+L' (b) cf(x)→cL (c) f(x)g(x)→LL' as x→a (d) if further L'≠0 then g(x)≠0 f…

Evaluate the  limits: SOLUTION  : by substituting the limit directly we are going to obtain zero(0) which shows that the limit does not exist.

In probability theory , Chebyshev's inequality guarantees that, for a wide class of probability distributions , "nearly all" values are close to the mean —…

Bernoulli Trials: the Bernoulli trial states that if there are two independent trials with two outcomes. Either True or False , Yes or No , Success or Failure , and …

Bhāskara II also known as Bhāskarāchārya or "Bhāskara the teacher" is an Indian mathematician and astronomer. his works represent a significant contribution t…

Examine whether The Mean Value Theorem(M.V.T) is applicable to the following functions for the interval in which they are defined.    SOLUTION: the f…

Theorem: The Mean Value Theorem States that let a real valued function f be continous on a closed interval [a,b] and differentiable in the open interval (a,b) then th…