Consider the following 2 × 2 matrix \(A\) where two elements are unknown and…

Consider the following 2 × 2 matrix $A$ where two elements are unknown and are marked by $a$ and $b$. The eigenvalues of this matrix are -1 and 7. What are the values of $a$ and $b$?

$\qquad A = \begin{pmatrix}1 & 4\\ b&a \end{pmatrix}$