Menu Close

A-2-1-1-3-1-2-2-1-2-find-the-inverse-of-this-matrix-

Tinku Tara 0 Comments
Pin




Question Number 141193 by Eric002 last updated on 16/May/21
A= [((2 ),1,(−1)),((−3),(−1),2),((−2),1,2) ]find the inverse of this matrix
A=[21−1−3−12−212]findtheinverseofthismatrix
Answered by bramlexs22 last updated on 16/May/21
Cayley−Hamilton theorem ∣A−λI∣ = 0 ⇒λ^3 −(tr A)λ^2 + (((minor of the terms)),((on the leading diagonal of A)) ) λ−det(A)=0 ⇒λ^3 −3λ^2 −λ−1=0 ⇒p(A)= 0 ⇒ [A^3 −3A^2 −A−I= 0 ]×A^(−1) ⇒A^2 −3A−I−A^(−1) = 0 ⇒A^(−1) = A^2 −3A−I
Cayley−Hamiltontheorem∣A−λI∣=0⇒λ3−(trA)λ2+(minorofthetermsontheleadingdiagonalofA)λ−det(A)=0⇒λ3−3λ2−λ−1=0⇒p(A)=0⇒[A3−3A2−A−I=0]×A−1⇒A2−3A−I−A−1=0⇒A−1=A2−3A−I
Commented by Eric002 last updated on 16/May/21
well done sir
welldonesir

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *