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किसी रैखिक समय-अपरिवर्तनीय निरंतर-समय प्रणाली का प्रणाली आव्यूह द्वारा दिया जाता है। अभिलक्षण समीकरण के मूलों के मान क्या होगें?

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  1. -1, -4
  2. -1, -5
  3. -4, -5
  4. 0, -1

Answer (Detailed Solution Below)

Option 1 : -1, -4
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परिकल्पना :

अभिलक्षण समीकरण के मूल के लिए :

[ sI - A ] = 0

जहाँ 

I = इकाई आव्यूह 

A = दिया गया आव्यूह 

व्याख्या:

दिया है 

अभिलक्षण समीकरण के मूल के लिए:

[sI - A] = 0

s( s + 5 ) + 4 = 0

s2 + 5s + 4 = 0

( s+4 )( s+1 ) = 0

s = -4, -1 

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