Question

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

2x - 3y = 19
x + 2y = -1
he multiplies the left side of the coefficient matrix by the inverse matrix.

how does he proceed to the solution?​

Answer 1

Explanation:

`\begin{bmatrix}2 & -3\\ 1 & 2\end{bmatrix}^(-1)* \begin{bmatrix}2 & -3\\ 1 & 2\end{bmatrix}* \begin{bmatrix}x\\y \end{bmatrix}=(1)/(7) \begin{bmatrix}2 & 3 \\ -1 & 2\end{bmatrix}* \begin{bmatrix}19\\ -1\end{bmatrix}`

Since,
`\begin{bmatrix}2 & -3\\ 1 & 2\end{bmatrix}^(-1)=(1)/(7)\begin{bmatrix}2 & 3\\ -1 & 2\end{bmatrix}`

And
`A^(-1)A=I`

`\begin{bmatrix}x\\y \end{bmatrix}=(1)/(7)\begin{bmatrix}2 & 3\\ -1 & 2\end{bmatrix}* \begin{bmatrix}19\\-1 \end{bmatrix}`

`\begin{bmatrix}x\\y \end{bmatrix}=(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.