Question

1. (20 points) Diagonalize A, and use the diagonalization to come up with an explicit formula for Ak where k is a nonnegative integer: [ 3 -11 A=

Answer 1

INDIAN GAILWAY Given Matej, A-li-42 → first we diagonalise A:- for such we find am inuectible Matein p which is toured by @jgenueclaes. .. find eigen ualues la dil co (3-2) (-2-d) +40 -6-3dt adta 4400 d²d-250 - d² adtd-2-0 ad(d-2)+(d-2)=0 (d-2)(at)=0 at d=a14 for dl , eigenuectal Liis (AdI] L U1] = 0 7 (945) "iL] -18] (4 1 3 4 = [0] wing=0

एक कदम स्वच्छता की ओर WIRE for d=d, eikenue Farbtong rat Abhiyan TA-ZI / V2 = 0 Eld. [454]["}]=[%] & 2, H2=0 1 PL - 12 - 11] - PCB, vs] = [41] P4= (adje)" + 6*1*:41] pt = flut] None, to final diagonal Matein ot As ptop = (14)[972] [4 15% ['$+][41]?1/3J I PHAP = 1 1 0 = 0 ] which is the lequüed diagonal Matun of A whose diagonal entues centain eigen ualues. N.R

IND NDIANA RAILWA WAYS PHAP =D A=POPT find formula for nk by wing diagonalisation, A2 = (PPP) (PDP 1) = PD (PIP) OPT = POPpt A = (POPP1) (PDP) = POP (PTP) Dpt= Poppy - AK = PO* p =${"13/ok. ID 41 AR = S-CR44 2k l ak 2 L-4 HJK + 4.2K UHDR-ak which is the required famula fal Ak by using Diagonalisation.