Determinants Matrices Question 78
Question: If $ A \begin{bmatrix} 1 & 2 \\ 3 & 5 \\ \end{bmatrix} , $ then the value of the determinant $ |A^{2009}-5A^{2008}| $ is
Options:
A) $ -6 $
B) $ -5 $
C) $ -4 $
D) $ 4 $
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] Given, $ A= \begin{bmatrix} 1 & 2 \\ 3 & 5 \\ \end{bmatrix} $
$ \Rightarrow | A |=5-6=-1 $
$ \therefore | A^{2009}-5A^{2008} |=| A^{2008} || A-5I | $
$ ={{(-1)}^{2008}}| \begin{bmatrix} 1 & 2 \\ 3 & 5 \\ \end{bmatrix} - \begin{bmatrix} 5 & 0 \\ 0 & 5 \\ \end{bmatrix} |= \begin{vmatrix} -4 & 2 \\ 3 & 0 \\ \end{vmatrix}=-6 $
BETA
