Determinants Matrices Question 125
Question: If matrix $ A= \begin{bmatrix} -5 & -8 & 0 \\ 3 & 5 & 0 \\ 1 & 2 & -1 \\ \end{bmatrix} $ then find $ tr(A)+tr(A^{2})+tr(A^{3})+…+tr(A^{100}) $
Options:
A) 100
B) 50
C) 200
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] Consider $ A^{2}= \begin{bmatrix} -5 & -8 & 0 \\ 3 & 5 & 0 \\ 1 & 2 & -1 \\ \end{bmatrix} \begin{bmatrix} -5 & -8 & 0 \\ 3 & 5 & 0 \\ 1 & 2 & -1 \\ \end{bmatrix} $
$ = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} =ISoA^{3}= \begin{bmatrix} -5 & -8 & 0 \\ 3 & 5 & 0 \\ 1 & 2 & -1 \\ \end{bmatrix} $ and So on $ tr(A)+tr(A^{2})tr(A^{3})+…+tr(A^{100}) $
$ =(-1)+(3)+(-1)+(3)+…+(-1)+(3)=200 $
BETA
