A-1-1-4-2-A-2016- Tinku Tara June 3, 2023 Matrices and Determinants 0 Comments FacebookTweetPin Question Number 11035 by suci last updated on 08/Mar/17 A=[1−1−4−2]A2016=…..? Answered by diofanto last updated on 19/Jul/17 FindingtheeigenvaluesofA:|1−λ−1−4−2−λ|=0(1−λ)(−2−λ)−4=0λ2+λ−6=0λ1=2,λ2=−3Findinganeigenvectorforeacheigenvalue:Ax=λ1x⇔(A−λ1I)x=0⇔[−1−1−4−4][x1x2]=[00]⇔x1=−x2,e.g.[−11]Ay=λ2y⇔(A−λ2I)y=0⇔[4−1−41][y1y2]=[00]⇔y1=y2/4,e.g.[14]Diagonalizing:A=[−1114][200−3][−1114]−1Finding[−1114]−1:(−11101401)∼(−11100511)∼(−104/5−1/50511)∼(10−4/51/5011/51/5)⇔[−1114]−1=[−4/51/51/51/5]A2016=[−1114][2201600(−3)2016][−4/51/51/51/5]… Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: u-1-1-2-A-3-2-1-3-0-1-v-2-1-uAv-t-Next Next post: how-do-you-find-the-least-value-of-x-2-2xy-3y-2-6x-2y-using-the-concepts-of-algebra-or-calculus- Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.