Category: Matrices and Determinants

Question Number 5963 by Ashis last updated on 07/Jun/16 $$\mathbf{for}\mathbf{what}\mathbf{value}\mathbf{of}\mathbf{k}\mathbf{the}\mathbf{system}\mathbf{of}\mathbf{equation}\mathbf{has}\mathbf{no}\mathbf{solution}$$$$\mathbf{x}+2\mathbf{y}+3\mathbf{z}=1$$$$2\mathbf{x}+\mathbf{ky}+5\mathbf{z}=1$$$$3\mathbf{x}+4\mathbf{y}+7\mathbf{z}=1$$ Commented by Yozzii last updated on 07/Jun/16…

Question Number 136457 by byaw last updated on 22/Mar/21 Commented by mr W last updated on 22/Mar/21 $$A,B,Caretrue.$$$$questionDisnotclear.oneangle$$$$alonecannotbecomplementary.$$$${if}\:{question}\:{D}\:{means}\:{that}\:{the}\:{angle} \…

Question Number 4638 by Yozzii last updated on 17/Feb/16 $$Let\mathbf{P}=\left(\begin{array}{cc}1-p_1& p_2\\ p_1& 1-p_2\end{array}\right)=\left(\begin{array}{cc}{a}_{1,1}& a_{1,2}\\ a_{2,1}& a_{2,2}\end{array}\right)$$$$andthat{\mathbf{P}}^{n}bethenthpowerof\mathbf{P}evaluated$$$${as}\:\boldsymbol{\mathrm{P}}^{{n}} =\boldsymbol{\mathrm{P}}×\boldsymbol{\mathrm{P}}^{{n}−\mathrm{1}} ;{i}.{e}\:{by}\:{successive}\:…

Question Number 135467 by benjo_mathlover last updated on 13/Mar/21 Answered by EDWIN88 last updated on 13/Mar/21 $$\left|\begin{array}{c}\alpha \beta \gamma \\ \beta \gamma \alpha \\ \gamma \alpha \beta \end{array}\right|=\alpha (\beta \gamma -{\alpha }^2)-\beta ({\beta }^2-\alpha \gamma )+\gamma (\alpha \beta -{\gamma }^2)$$$$=\alpha\beta\gamma−\alpha^{\mathrm{3}} −\beta^{\mathrm{3}} +\alpha\beta\gamma+\alpha\beta\gamma−\gamma^{\mathrm{3}} \…

Question Number 3965 by Yozzii last updated on 25/Dec/15 $$Finddet\left(A\right)whereAisann\times nmatrix$$$$oftheform$$$$A=\left(\begin{array}{cccccccc}\lambda & 1& 1& \dots & \dots & \dots & \dots & 1\\ 1& \lambda & 1& \dots & \dots & \dots & \dots & 1\\ 1& 1& \lambda & \dots & \dots & \dots & \dots & 1\\ ⋮& ⋮& ⋮& \ddots & \dots & \dots & \dots & 1\\ ⋮& ⋮& ⋮& ⋮& \ddots & \dots & \dots & 1\\ ⋮& ⋮& ⋮& ⋮& ⋮& \ddots & \dots & 1\\ ⋮& ⋮& ⋮& ⋮& ⋮& ⋮& \ddots & 1\\ 1& 1& 1& 1& 1& 1& 1& \lambda \end{array}\right)$$$$\lambda =constantforleadingdiagonalelements$$$$1sforallotherelements.$$$$$$ Commented by 123456…