Question

5. Which matrix equation can be used to solve the system?f6x+ 7y - 1417x+By - 27021-41M[1-1-02)CHEM-6276 | 27

Answer 1

The system of equations:

`\begin{gathered} 6x+7y=14 \\ 7x+8y=27 \end{gathered}`

can be written as:

`\begin{bmatrix}6 & 7 \\ 7 & 8\end{bmatrix}\begin{bmatrix}x \\ y\end{bmatrix}=\begin{bmatrix}14 \\ 27\end{bmatrix}`

To find the solution we need to find the inverse matrix of the coefficients matrix. For a two by two matrix the inverse is given as:

`\frac{1}{\mbox{det }A}\begin{bmatrix}d & -b \\ -c & a\end{bmatrix}`

Then in this case the inverse matrix is