find-all-2×2-matrices-A-such-that-A-3-3A-2-2-2-2-2- Tinku Tara June 4, 2023 Matrices and Determinants 0 Comments FacebookTweetPin Question Number 100650 by bobhans last updated on 28/Jun/20 findall2×2matricesAsuchthatA3−3A2=(−2−2−2−2) Answered by bramlex last updated on 28/Jun/20 letA=(abcd)A2(A−3I)=(−2−2−2−2)(det(A))2det(A−3I)=det(−2−2−2−2)=0case1det(A)=0⇒p(λ)=det(λI−A)=0|λ−a−b−cλ−d|=λ2−(a+d)λ+ad−bcλ2−TR(A)λ+det(A)=0⇒λ2−TR(A)λ=0;A2=TR(A).AA3=A(TR(A))=(TR(A))2A⇒A3−3A=(−2−2−2−2)TR(A)3−3(TR(A))2+4=0TR(A)=2orTR(A)=−1case1aTR(A)=2⇒−2A=(−2−2−2−2)A=(1111).TR(A)=−14A=(−2−2−2−2)⇒A=(−12−12−12−12)case2det(A−3I)=0det(A−2I)2(A+I)=0case2adet(A−2I)=0⇒p(λ)=λ2−5λ+6A2=5A−6I⇒A3−3A2=(19A−30I)−3(5A−6I)=4A−12I=(−2−2−2−2)4A=(10−2−210)⇒A=(52−12−1252)case2bdet(A+I)=0⇒p(λ)=λ2−2λ−3A2−2A−3I=0;A2=2A+3IA3−3A2=7A+6I−3(2A+3I)=A−3I⇒A−3I=(−2−2−2−2)A=(1−2−21)∴A=(1111);(−12−12−12−12);(52−12−1252);(1−2−21) Commented by bobhans last updated on 28/Jun/20 great=== Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: if-sin-1-2-find-cos-Next Next post: Question-100653 Leave a Reply Cancel replyYour email address will not be published.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.