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Question Number 98661 by bemath last updated on 15/Jun/20
usingcayley−hamiltontheoremwhatistheinverseofmatrixA=[01−112201−1]
Commented by john santu last updated on 15/Jun/20
wefirstcomputethecharacteristicequation∣A−λI∣=0[−λ1−112−λ201−1−λ]=0=−λ{(2−λ)(−1−λ)−2}−(−1−λ)−1=λ{λ2−λ−4}+1+λ−1=λ3−λ2−3λthecayley−hamiltontheoremstatesthatamatrixsatisfiesitsowncharacteristicequation⇒A3−A2−3A=0A(A2−A−3I)=0⇔I=13A(A−I)⇔A−1=13(A−I)⇔A−1=13[−11−111201−2]
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