Determinants Matrices Question 156
Question: Let $ A= \begin{bmatrix} 0 & \alpha \\ 0 & 0 \\ \end{bmatrix} $ and $ {{(A+I)}^{50}}-50A= \begin{bmatrix} a & b \\ c & d \\ \end{bmatrix} , $ find $ abc+abd+bcd+acd $
Options:
A) 0
B) -1
C) 1
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] As $ A^{2}=0,A^{k}=0\forall k\ge 2 $ . Thus, $ {{(A+I)}^{50}}=I+50A\Rightarrow {{(A+I)}^{50}}-50A=I $
$ \therefore a=1,b=0,c=0,d=1 $
$ abc + abd + bcd + acd = 0 $
BETA
