Category: Matrices and Determinants

Question Number 54952 by gunawan last updated on 15/Feb/19 $$\mathrm{If}T:\mathbb{C}\to \mathbb{C}\mathrm{is}\mathrm{linear}\mathrm{transformation}$$$$\mathrm{and}x\in \mathbb{C},\mathrm{then}T\left(x\right)=\dots$$ Commented by kaivan.ahmadi last updated on 15/Feb/19 $$letx=ai+bthen$$$${T}\left({x}\right)={T}\left({ai}+{b}\right)={T}\left({ai}\right)+{T}\left({b}\right)= \…

Question Number 54938 by gunawan last updated on 14/Feb/19 $$\mathrm{If}A=\left[\begin{array}{cc}2& 1\\ 1& 2\end{array}\right],\mathrm{then}{A}^{2006}=\dots$$ Commented by Abdo msup. last updated on 15/Feb/19 $$wehaveA=\left(\begin{array}{c}20\\ 02\end{array}\right)+\left(\begin{array}{c}01\\ 10\end{array}\right)=2I+J$$$${J}^{\mathrm{2}} =$$\left(\begin{array}{c}01\\ 10\end{array}\right)$$\:.$$\left(\begin{array}{c}01\\ 10\end{array}\right)$$\:=$$\left(\begin{array}{c}10\\ 01\end{array}\right)$$\:={I}\:\Rightarrow…

Question Number 54903 by Meritguide1234 last updated on 14/Feb/19 Answered by kaivan.ahmadi last updated on 14/Feb/19 $$\det \left({\mathrm{ABA}}^{\mathrm{T}}\right)=\det \left({\mathrm{A}}^2\mathrm{B}\right)={\mathrm{detA}}^2\mathrm{detB}=8\left(\mathrm{i}\right)$$$$\det \left({\mathrm{AB}}^{-1}\right)=\frac{\mathrm{detA}}{\mathrm{detB}}=8\Rightarrow \mathrm{detA}=8\mathrm{detB}\left(\mathrm{ii}\right)$$$$\mathrm{replace}\:\left(\mathrm{ii}\right)\:\mathrm{in}\:\left(\mathrm{i}\right)\:\mathrm{deduce}…

Question Number 54644 by gunawan last updated on 08/Feb/19 $$\mathrm{A}=\left[\begin{array}{cc}3& 7\\ -1& -2\end{array}\right]$$$$A^{27}+A^{31}+A^{40}=\dots$$ Answered by kaivan.ahmadi last updated on 10/Feb/19 $$\mathrm{A}^{\mathrm{2}}…

Question Number 118640 by 281981 last updated on 18/Oct/20 Answered by MJS_new last updated on 19/Oct/20 $$1)$$$$x=-2\wedge y=0\mathrm{solves}\mathrm{all}\mathrm{given}\mathrm{equations}$$ Answered by 1549442205PVT last…