como se faz matriz inversa ?
4 2
3 4
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Primero halla la matriz de cofactores
![C_{11}=(-1)^{1+1}(4)=4\hspace{1cm} C_{12}=(-1)^{1+2}(3)=-3\\ \\
C_{21}=(-1)^{2+1}(2)=-2\hspace{1cm} C_{22}=(-1)^{2+2}(4)=4\\ \\ \\
C=\left[\begin{matrix}
4&-3\\-2&4
\end{matrix}\right]\\ \\ \\
\text{Luego el determinante:}\\ \\
|A|=\left|\begin{matrix}
4&2\\3&4
\end{matrix}\right|=(4)(4)-(2)(3) = 10](https://tex.z-dn.net/?f=C_%7B11%7D%3D%28-1%29%5E%7B1%2B1%7D%284%29%3D4%5Chspace%7B1cm%7D+C_%7B12%7D%3D%28-1%29%5E%7B1%2B2%7D%283%29%3D-3%5C%5C+%5C%5C%0AC_%7B21%7D%3D%28-1%29%5E%7B2%2B1%7D%282%29%3D-2%5Chspace%7B1cm%7D+C_%7B22%7D%3D%28-1%29%5E%7B2%2B2%7D%284%29%3D4%5C%5C+%5C%5C+%5C%5C%0AC%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D%0A4%26amp%3B-3%5C%5C-2%26amp%3B4%0A%5Cend%7Bmatrix%7D%5Cright%5D%5C%5C+%5C%5C+%5C%5C%0A%5Ctext%7BLuego+el+determinante%3A%7D%5C%5C+%5C%5C%0A%7CA%7C%3D%5Cleft%7C%5Cbegin%7Bmatrix%7D%0A4%26amp%3B2%5C%5C3%26amp%3B4%0A%5Cend%7Bmatrix%7D%5Cright%7C%3D%284%29%284%29-%282%29%283%29+%3D+10%0A "C_{11}=(-1)^{1+1}(4)=4\hspace{1cm} C_{12}=(-1)^{1+2}(3)=-3\\ \\
C_{21}=(-1)^{2+1}(2)=-2\hspace{1cm} C_{22}=(-1)^{2+2}(4)=4\\ \\ \\
C=\left[\begin{matrix}
4&-3\\-2&4
\end{matrix}\right]\\ \\ \\
\text{Luego el determinante:}\\ \\
|A|=\left|\begin{matrix}
4&2\\3&4
\end{matrix}\right|=(4)(4)-(2)(3) = 10")
![A^{-1}=\dfrac{\left[\begin{matrix}
4&-3\\-2&4
\end{matrix}\right]^t}{|A|}\\ \\ \\
A^{-1}=\dfrac{\left[\begin{matrix}
4&-2\\-3&4
\end{matrix}\right]}{10}\\ \\ \\
\boxed{\boxed{A^{-1}=\left[\begin{matrix}
4/10&-2/10\\-3/10&4/10
\end{matrix}\right]}}](https://tex.z-dn.net/?f=A%5E%7B-1%7D%3D%5Cdfrac%7B%5Cleft%5B%5Cbegin%7Bmatrix%7D%0A4%26amp%3B-3%5C%5C-2%26amp%3B4%0A%5Cend%7Bmatrix%7D%5Cright%5D%5Et%7D%7B%7CA%7C%7D%5C%5C+%5C%5C+%5C%5C%0AA%5E%7B-1%7D%3D%5Cdfrac%7B%5Cleft%5B%5Cbegin%7Bmatrix%7D%0A4%26amp%3B-2%5C%5C-3%26amp%3B4%0A%5Cend%7Bmatrix%7D%5Cright%5D%7D%7B10%7D%5C%5C+%5C%5C+%5C%5C%0A%5Cboxed%7B%5Cboxed%7BA%5E%7B-1%7D%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D%0A4%2F10%26amp%3B-2%2F10%5C%5C-3%2F10%26amp%3B4%2F10%0A%5Cend%7Bmatrix%7D%5Cright%5D%7D%7D "A^{-1}=\dfrac{\left[\begin{matrix}
4&-3\\-2&4
\end{matrix}\right]^t}{|A|}\\ \\ \\
A^{-1}=\dfrac{\left[\begin{matrix}
4&-2\\-3&4
\end{matrix}\right]}{10}\\ \\ \\
\boxed{\boxed{A^{-1}=\left[\begin{matrix}
4/10&-2/10\\-3/10&4/10
\end{matrix}\right]}}")
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