1. Tardigrade
  2. Question
  3. Mathematics
  4. If A=[1 2 3 5] then the value of the determinant |A2018-5 A2017| is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $A=\begin{bmatrix}1 & 2 \\ 3 & 5\end{bmatrix}$ then the value of the determinant $\left|A^{2018}-5 A^{2017}\right|$ is equal to

Determinants

Solution:

$\Theta|A|=-1 $
$\therefore\left|A^{2018}-5 A^{2017}\right|=|A|^{2017}|A-5 I|$
$=(-1)^{2017}\left|\begin{bmatrix} -4 & 2 \\ 3 & 0 \end{bmatrix}\right|=(-1)(-6)=6$