Category: Matrices and Determinants

Question Number 81906 by ahmadshahhimat775@gmail.com last updated on 16/Feb/20 Commented by mr W last updated on 16/Feb/20 $$w{hat}^{\prime }sthedifferencebetween2)and4)?$$ Terms of Service Privacy Policy…

Question Number 80830 by jagoll last updated on 07/Feb/20 $$givenAasquarematrixnon$$$$singularA\ne I.$$$$findAsuchthat{A}^3=I$$ Answered by ~blr237~ last updated on 07/Feb/20 $${M}={diag}\left(\mathrm{1},{j},\overset{−}…

Question Number 78670 by berket last updated on 19/Jan/20 $$letA=\left[\begin{array}{c}ab\\ cd\end{array}\right]usetheaugmentedmatrix\left[AI\right]andelementaryrowoperationtoshow{A}^{-1}=\frac{1}{adbc}\left[\begin{array}{c}ab\\ cd\end{array}\right]andshowthatdet\left(A^{-1}\right)=\frac{1}{det\left(A\right)}$$$$$$ Commented by abdomathmax last updated on 20/Jan/20 $${Pc}\left({A}\right)={det}\left({A}−{xI}\right)\:=$$\left|\begin{array}{c}a-xb\\ cd-x\end{array}\right|$$ \…

Question Number 346 by 123456 last updated on 25/Jan/15 $$\mathrm{\Gamma }\left(\theta \right)=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]$$$$\mathrm{\Lambda }(\theta ,t)=\left[\begin{array}{cc}\cos \theta & \sinh t\sin \theta \\ \sin \theta & \cosh t\cos \theta \end{array}\right]$$$$\zeta (\theta ,t)=\mathrm{\Gamma }\left(\theta \right)\times \mathrm{\Lambda }(\theta ,t)+\mathrm{\Lambda }(\theta ,t)\times \mathrm{\Gamma }\left(\theta \right)$$$$\zeta (\theta ,0)=?$$$$\det \zeta (\theta ,0)=?$$ Answered by prakash jain last…

Question Number 15 by user1 last updated on 25/Jan/15 $$\mathrm{If}A=\left[\begin{array}{cc}3& -5\\ -4& 2\end{array}\right],$$$$\mathrm{show}\mathrm{that}{A}^2-5A-14I=0$$ Answered by user1 last updated on 30/Oct/14 $$\mathrm{We}\mathrm{have}:$$$${A}^{\mathrm{2}}…