Category: Algebra

Question Number 50369 by prof Abdo imad last updated on 16/Dec/18 $$findx,yfromZwichverify$$$$y^2=x(x+1)(x+7)(x+8)$$ Answered by mr W last updated on 16/Dec/18…

Question Number 50368 by prof Abdo imad last updated on 16/Dec/18 $$findall(x,y)\in Q^{+{★}^2}and{x}^y=y^{x}andx<y$$ Commented by mr W last updated on…

Question Number 50366 by prof Abdo imad last updated on 16/Dec/18 $$letA=\left(\begin{array}{c}0m{m}^2\\ \frac{1}{m}0m\end{array}\right)$$$$\left(\frac{1}{m^2}\frac{1}{m}0\right)$$$$A\in M_3\left(R\right)andmnot0$$$$1)findrelationbetwen{I}_3,Aand{A}^2$$$$\left.\mathrm{2}\right)\:{is}\:{A}\:{inversible}\:\:\:.{determine}\:{A}^{−\mathrm{1}} \:{in}\:{case}\:{of}\:{exist}…

Question Number 50365 by prof Abdo imad last updated on 16/Dec/18 $$letJ=\left[\begin{array}{c}111\\ 111\end{array}\right]$$$$\left[\begin{array}{c}111\\ \end{array}\right]$$$$elementof{M}_3\left(R\right)$$$$find{J}^n$$$$$$ Terms of…

Question Number 50363 by prof Abdo imad last updated on 16/Dec/18 $$letp\in K_n\left[x\right]sndAandHtworlementsofK\left[x\right]$$$$1)provethatp(A\left(x\right)+H\left(x\right))=\sum _{k=0}^n\frac{p^{\left(k\right)}\left(A\left(x\right)\right)}{k!}.{\left(H\left(x\right)\right)}^k$$$$2)findtheconditionthatp(A\left(x\right)+H\left(x\right))is$$$$dividedbyH\left(x\right)\ne 0$$$$\left.\mathrm{3}\right)\:{if}\:{p}\left({x}\right)\neq{c}\:{prove}\:\:{that}\:{p}\left({p}\left({x}\right)\right)−{x}\:{is}\:{divided} \…