Previous in Matrices and Determinants Next in Matrices and Determinants
Question Number 175265 by oustmuchiya@gmail.com last updated on 25/Aug/22
$$\mathrm{Given}\:\mathrm{that}\:\mathrm{matrix}\: \\ $$$$\mathrm{B}=\begin{cases}{\:\:\sqrt{\mathrm{3}}}\\{-\sqrt{\mathrm{5}}}\end{cases}\left.\begin{matrix}{\:\:\:\:\sqrt{\mathrm{2}}}\\{\:\:\:\:\sqrt{\mathrm{7}}}\end{matrix}\right\}\:\mathrm{find}\: \\ $$$$\mathrm{B}^{-\mathrm{1}} \:\mathrm{using}\:\mathrm{row}\:\mathrm{operation} \\ $$
Answered by CElcedricjunior last updated on 25/Aug/22
$$\boldsymbol{{det}}\left(\boldsymbol{{B}}\right)=\sqrt{\mathrm{21}}+\sqrt{\mathrm{10}} \\ $$$$\boldsymbol{{B}}^{−\mathrm{1}} =\frac{\mathrm{1}}{\:\sqrt{\mathrm{21}}+\sqrt{\mathrm{10}}}\begin{pmatrix}{\sqrt{\:\mathrm{7}}\:\:\:\:\:−\:\sqrt{\:\mathrm{2}}}\\{\sqrt{\:\mathrm{5}}\:\:\:\:\:\:\:\:\sqrt{\mathrm{3}}}\end{pmatrix} \\ $$$$\: \\ $$$$\:.......\boldsymbol{{le}}\:\boldsymbol{{celebre}}\:\boldsymbol{{cedric}}\:\boldsymbol{{junior}}....... \\ $$$$ \\ $$