A) 8
B) 12
C) 13
D) 7
Correct Answer: A
Solution :
We have \[(A-3I)(A-5I)=O\] \[{{A}^{2}}-8A+15I=O\] Multiplying both sides with \[{{A}^{-1}}\], we get \[A-8I+15{{A}^{-1}}=O\] \[A+15{{A}^{-1}}=8I\] \[\frac{A}{2}+\frac{15{{A}^{-1}}}{2}=4I\] \[\therefore \alpha +\beta =\frac{1}{2}+\frac{15}{2}=\frac{16}{2}=8\]You need to login to perform this action.
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