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If A = [(1,2,3,4)], then A^4 – 5A^3 – A^2 – 4A – I =

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If A  = [(1,2,3,4)],  then A4 – 5A3 – A2 – 4A – I =

(a)  0 

(b)  I 

(c)  A 

(d)  A + I 

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1 Answer

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Best answer

Correct option    (d)  A + I 

Explanation:

The characteristic equation is

λ2 – 5λ – 2 = 0

A2 5A  – 2I = 0

A3 = 5A2 + 2IA

A4 = 5A3 + 2IA2 

A4 – 5A3 – A2 = A2 = 5A + 2I

A4 –5A3 – A2 – 4A – I = A + I

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