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Question Number 57790 by pete last updated on 12/Apr/19

$$\mathrm{Given}\mathrm{N}=\left[\begin{array}{c}53\\ 64\end{array}\right]\mathrm{and}\mathrm{P}=\left[\begin{array}{c}4-3\\ -65\end{array}\right],$$$$\mathrm{find}\mathrm{NP}\mathrm{and}\mathrm{deduce}\mathrm{the}\mathrm{inverse}\mathrm{of}\mathrm{P}.$$

Answered by math1967 last updated on 12/Apr/19

$$\left[\begin{array}{cc}5& 3\\ 6& 4\end{array}\right]\left[\begin{array}{cc}4& -3\\ -6& 5\end{array}\right]=\left[\begin{array}{cc}20-18& -15+15\\ 24-24& -18+20\end{array}\right]$$$$\left[\begin{array}{cc}2& 0\\ 0& 2\end{array}\right]=2I$$$$\therefore NP=2I\Rightarrow {NPP}^{-1}=2{IP}^{-1}$$$$\Rightarrow NI=2P^{-1}\therefore 2P^{-1}=N$$$$\therefore P^{-1}=\left[\begin{array}{cc}2& \frac{-3}{2}\\ -3& \frac{5}{2}\end{array}\right]$$

Commented by pete last updated on 12/Apr/19

$$\mathrm{Thanks}\mathrm{so}\mathrm{much}$$

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