Question

a Matriz inversa de A = [ 1 2 0 | 1 3 0 | 0 1 -1/6]
$1 \: \: \: \: 2 \: \: \: 0 \\ 1 \: \: \: \: 3 \: \: \: \: 0 \\ 0 \: \: \: \: 1 \: \: \frac{ - 1}{6}$
.. É uma matriz de ordem 3X3 .. me ajudem a achar a Matriz inversa pfvor​

Answer 1

Bom Dia!

Veja a explicação:

Temos de antes relembrar conceitos:

• Regra de Saurrus
• Matriz Adjunta
• Matriz Inversa

Matriz Primordial:

$\displaystyle \left[\begin{array}{ccc}1&2&0\\1&3&0\\0&1&\dfrac{-1}{6} \end{array}\right]$

$A^{-1}$:

$\displaystyle \left[\begin{array}{ccc}1&2&0\\1&3&0\\0&1&\dfrac{-1}{6} \end{array}\right | \left\begin{array}{ccc}1&2&\\1&3&\\0&1&\end{array}\right$

$\boxed { \dfrac{2}{6}} \Longleftrightarrow \boxed {\dfrac{-3}{6}} \\ \\ D= \dfrac{-1}{6}$

$\displaystyle \left[\begin{array}{ccc}1&2&0\\1&3&0\\0&1&\dfrac{-1}{6} \\1&2&0 \\ 1&3&0\end{array}\right \| \left\begin{array}{ccc}1&2&\\1&3&\\0&1&\\1&2\\ 1&3\end{array}\right$

$A_{aj} = \displaystyle \left(\begin{array}{ccc}\dfrac{-3}{6} &\dfrac{2}{6} &0 \\ \\ \dfrac{1}{6} &\dfrac{-1}{6} &0\\1&-1&1\end{array}\right)$

$\boxed { A^{-1} = \displaystyle \left(\begin{array}{ccc}\dfrac{-3}{6} &\dfrac{2}{6} &0 \\ \\ \dfrac{1}{6} &\dfrac{-1}{6} &0\\1&-1&1\end{array}\right) }$

• Att. MatiasHP