Question 16.6.5: Solve the following system of equations by using Theorem 16.......

Suppose we define the matrices

Then the system is equivalent to the matrix equation Ax = b. Because |A| = 2 \neq 0, matrix A has an inverse, and according to Theorem 16.6.2, x = A^{−1}b. Hence,

where we have used Eq. (16.6.3) to find A^{−1}. The solution is therefore x = 1, y = 1.^{8}

A=\begin{pmatrix} a & b \\ c & d \end{pmatrix} \Rightarrow A^{-1}=\frac{1}{ad-bc} \begin{pmatrix} d & b \\ -c & a \end{pmatrix}          (16.6.3)

^{8} Check by substitution that this really is the correct solution. Clearly, it is easier to solve the system by subtracting the first equation from the second to obtain y = 1, and so x = 1.