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diagonalizar $$$\left[\begin{array}{cc}3 & -10\\1 & -4\end{array}\right]$$$
Sua entrada
Diagonalizar $$$\left[\begin{array}{cc}3 & -10\\1 & -4\end{array}\right]$$$.
Solução
Primeiro, encontre os autovalores e autovetores (para ver as etapas, consulte calculadora de autovalores e autovetores).
Autovalor: $$$1$$$, autovetor: $$$\left[\begin{array}{c}5\\1\end{array}\right]$$$.
Autovalor: $$$-2$$$, autovetor: $$$\left[\begin{array}{c}2\\1\end{array}\right]$$$.
Forme a matriz $$$P$$$, cuja coluna $$$i$$$ é o autovetor no. $$$i$$$: $$$P = \left[\begin{array}{cc}5 & 2\\1 & 1\end{array}\right]$$$.
Forme a matriz diagonal $$$D$$$ cujo elemento na linha $$$i$$$, coluna $$$i$$$ é o autovalor nº. $$$i$$$: $$$D = \left[\begin{array}{cc}1 & 0\\0 & -2\end{array}\right]$$$.
As matrizes $$$P$$$ e $$$D$$$ são tais que a matriz inicial $$$\left[\begin{array}{cc}3 & -10\\1 & -4\end{array}\right] = P D P^{-1}$$$.
Responder
$$$P = \left[\begin{array}{cc}5 & 2\\1 & 1\end{array}\right]$$$A
$$$D = \left[\begin{array}{cc}1 & 0\\0 & -2\end{array}\right]$$$A