Question

Transfer transfer the system of equations by forming a matrix equation.

Answer 1

Answer:

Step-by-step explanation:

$\begin{bmatrix}2 & -3\\ 1 & 2\end{bmatrix}^{-1}\times \begin{bmatrix}2 & -3\\ 1 & 2\end{bmatrix}\times \begin{bmatrix}x\\y \end{bmatrix}=\frac{1}{7} \begin{bmatrix}2 & 3 \\ -1 & 2\end{bmatrix}\times \begin{bmatrix}19\\ -1\end{bmatrix}$  

Since, $\begin{bmatrix}2 & -3\\ 1 & 2\end{bmatrix}^{-1}=\frac{1}{7}\begin{bmatrix}2 & 3\\ -1 & 2\end{bmatrix}$

And $A^{-1}A=I$

$\begin{bmatrix}x\\y \end{bmatrix}=\frac{1}{7}\begin{bmatrix}2 & 3\\ -1 & 2\end{bmatrix}\times \begin{bmatrix}19\\-1 \end{bmatrix}$

$\begin{bmatrix}x\\y \end{bmatrix}=\frac{1}{7}\begin{bmatrix}35\\ -21\end{bmatrix}$

$\begin{bmatrix}x\\y \end{bmatrix}=\begin{bmatrix}5\\ -3\end{bmatrix}$                

Therefore, x = 5 and y = -3 will be the value of variables.