A2(A−2I)−4(A−I)=0 A3−2A2−4A+4I=0 Multiply by A A4=2A3+4A2−4A A4=2(2A2+4A−4I)+4A2−4A A4=8A2+4A−8I Multiply again by A ⇒A5=8A3+4A2−8A ⇒A5=8(2A2+4A−4I)+4A2−8A ⇒A5=20A2+24A−32I Comparing with A5=αA2+βA+γl α=20,β=24,γ=−32 ∴α+β+γ=20+24−32 =44−32 =12
