Category: Matrices and Determinants

Question Number 100664 by bobhans last updated on 28/Jun/20 $$\mathrm{A}\:\mathrm{matrix}\:\mathrm{2×2}\:\&\:\mathrm{B}\:=\:\begin{pmatrix}{−\mathrm{2}\:\:\:\:\mathrm{3}}\\{\:\:\mathrm{2}\:\:\:\:\:\:\mathrm{4}}\end{pmatrix}\:\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{A}^{\mathrm{T}} \mathrm{B}+\mathrm{3A}^{\mathrm{T}} \:=\:\begin{pmatrix}{\:\:\:\mathrm{5}\:\:\:\:\mathrm{4}}\\{−\mathrm{1}\:\:\:\mathrm{1}}\end{pmatrix}\:\:\mathrm{so}\:\mathrm{find}\:\mathrm{det}\left(\mathrm{4A}^{−\mathrm{1}} \right) \\ $$ Answered by bramlex last updated on 28/Jun/20 $${A}^{{T}}…

Question Number 100296 by bobhans last updated on 26/Jun/20 $$\mathcal{G}\mathrm{iven}\:\mathrm{matrix}\:\mathrm{A}\:=\:\begin{bmatrix}{\mathrm{3}\:\:\:\:\:\mathrm{1}\:\:\:\:\:\mathrm{4}}\\{\mathrm{1}\:\:\:\:\:\mathrm{2}\:\:\:\:\:\:\mathrm{5}}\\{\mathrm{0}\:\:\:\:\:\mathrm{2}\:\:\:\:\:\mathrm{6}}\end{bmatrix} \\ $$$$\mathrm{find}:\:\:\mathrm{adj}\left(\mathrm{adj}\:\mathrm{A}\right)\:? \\ $$ Answered by bemath last updated on 26/Jun/20 $$\mathrm{adj}\left(\mathrm{adj}\:\mathrm{A}\right)\:=\:\mid\mathrm{A}\mid^{\mathrm{n}−\mathrm{1}} \:.\mathrm{A} \\ $$$$\mathrm{A}_{\mathrm{3}×\mathrm{3}}…

Question Number 100068 by  M±th+et+s last updated on 24/Jun/20 $${hello}\:{all}\:{i}\:{have}\:{some}\:{questions}? \\ $$$$ \\ $$$$\left.\mathrm{1}\right){what}\:{is}\:{the}\:{riemann}\:{hypothesis}? \\ $$$$ \\ $$$$\left.\mathrm{2}\right){how}\:{did}\:{they}\:{determine}\:{the}\:{distance} \\ $$$${to}\:{the}\:{sun}? \\ $$$$ \\ $$$$\left.\mathrm{3}\right){how}\:{did}\:{we}\:{measure}\:{the}\:{speed}\:{of}\:{light}? \\…

Question Number 34355 by srikarkailash9@gmail.com last updated on 05/May/18 Commented by math khazana by abdo last updated on 05/May/18 $${let}\:{prove}\:{by}\:{recurrence}\:{that}\: \\ $$$${A}^{{n}} \:=\:\begin{pmatrix}{{p}^{{n}} \:\:\:\:\:\:\:\:{q}\frac{{p}^{{n}} −\mathrm{1}}{{p}−\mathrm{1}}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix}…

Question Number 164133 by Avijit007 last updated on 14/Jan/22 Answered by cortano1 last updated on 15/Jan/22 $$\:{A}=\begin{bmatrix}{{a}\:\:\:\:{b}}\\{{c}\:\:\:\:{d}}\end{bmatrix};\:{B}=\begin{bmatrix}{{e}\:\:\:\:{f}}\\{{g}\:\:\:\:{h}}\end{bmatrix} \\ $$$$\:\begin{bmatrix}{\mathrm{2}{a}+\mathrm{3}{e}\:\:\:\:\mathrm{2}{b}+\mathrm{3}{f}}\\{\mathrm{2}{c}+\mathrm{3}{g}\:\:\:\:\:\mathrm{2}{d}+\mathrm{3}{h}}\end{bmatrix}=\:\begin{bmatrix}{\mathrm{8}\:\:\:\:\:\mathrm{3}}\\{\mathrm{7}\:\:\:\:\:\mathrm{6}}\end{bmatrix} \\ $$$$\:\begin{bmatrix}{{a}+{e}\:\:\:\:{b}+{g}}\\{{c}+{f}\:\:\:\:{d}+{h}}\end{bmatrix}=\:\begin{bmatrix}{\mathrm{3}\:\:\:\:\:\:\mathrm{1}}\\{\mathrm{3}\:\:\:\:\:\:\mathrm{3}}\end{bmatrix} \\ $$$$\:\mathrm{2}{a}+\mathrm{3}{e}=\mathrm{8}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}{d}+\mathrm{3}{h}=\mathrm{6} \\ $$$$\:\mathrm{2}{a}+\mathrm{2}{e}=\mathrm{6}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}{d}+\mathrm{2}{h}=\mathrm{6}…