Question

x+ 2y=3
3x + 4y = -2

a matriz inversa dos coeficientes​

Answer 1

$\begin{cases}x+2y=3\\3x+4y=-2\end{cases} \\=\begin{bmatrix}1&2\\3&4\end{bmatrix}\cdot\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}3\\-2\end{bmatrix}$

$\sf{M}=\begin{bmatrix}1&2\\3&4\end{bmatrix}\\\sf{det~M=1\cdot4-2\cdot3=4-6=-2}$

$\sf{cof~M}=\begin{bmatrix}4&-3\\-2&1\end{bmatrix}$

$\sf{Adj~M=cof~M^T}=\begin{bmatrix}4&-2\\-3&1\end{bmatrix}$

$\sf{M^{-1}}=\sf{\dfrac{1}{det~M}\cdot Adj(M)}$

$\sf{M^{-1}}=\sf{-\dfrac{1}{2}}\cdot\begin{bmatrix}4&-2\\-3&1\end{bmatrix}$

$\sf{M^{-1}}=\begin{bmatrix}-2&1\\\frac{3}{2}&-\frac{1}{2}\end{bmatrix}$