Hello all I learning about determinants and this problem currently has me completely stumped. I can not figure how the answer in the book was achieved.
Problem:
$\det(\lambda I_2 - A)$ where $$ A = \begin{bmatrix} 4 & 2 \\ -1 & 1\\ \end{bmatrix} $$
The book answer is: $ \lambda^2 - 5 \lambda + 6$
I could only figure out how the 6 was found. I would like to note we haven't gone over eigenvalues either.
Thanks.
There's nothing about eigenvalues here. It's a simple calculation: $$\lambda I_2 - A = \left[\array{\lambda - 4 & -2 \\ 1 & \lambda - 1}\right],$$
so its determinant is $(\lambda - 4)(\lambda - 1) + 2 = \lambda^2 - 5\lambda + 6$ by the standard determinant formula for $2\times 2$ matrices.