the characteristic equation of a (3X3) matrix P is defined as $$a(\lambda)=|\lambda I-P|=\lambda^3+\lambda^2+2 \lambda+I=0$$
if I denotes identity matrix then find the inverse of P

Question

the characteristic equation of a (3X3) matrix P is defined as $$a(\lambda)=|\lambda I-P|=\lambda^3+\lambda^2+2 \lambda+I=0$$
if I denotes identity matrix then find the inverse of P

ikram002p · Answer

*

sidsiddhartha · Answer

;}

sidsiddhartha · Answer

im thinking about carey hamilton

sidsiddhartha · Answer

every square matrix satisfies its characteristic equation so 
can i substitute
$$\lambda=P$$

ganeshie8 · Answer

$$\large P^3+P^2+2P+I = 0$$

like this ?

sidsiddhartha · Answer

yes it can be written right?

sidsiddhartha · Answer

@ganeshie8

ganeshie8 · Answer

definitely thats what cayley-hamilton theorem is about, right ?

sidsiddhartha · Answer

yeah
now if i multiply P^-1 in both sides i think i'll get a result

ganeshie8 · Answer

looks good to me but i need to look my notes lol, not really sure on these..

sidsiddhartha · Answer

yeah mee too i've done this 3 years ago and almost forgot everything lol

ganeshie8 · Answer

$$\large P^3+P^2+2P = -I$$

ganeshie8 · Answer

$$\large P^{-1}(P^3+P^2+2P = -I)$$

ganeshie8 · Answer

looks fine to me :)

sidsiddhartha · Answer

yeah $$P^{-1}=-(p^2+P+2I)$$

sidsiddhartha · Answer

yeah its one of the option okay thanks :)

ganeshie8 · Answer

nice :D