Let A= [ array cc 2 & -5 3 & 1 array ] , what is f(A)= ?, where f(x)=x^3-2 x^2-5 .

Step-by-step solution

aligned & (c) f(x)=x^3-2 x^2-5 , & then f(A)=A^3-2 A^2-5 I & A= [ array cc 2 & -5 3 & 1 array ] , then & A^2= [ array cc 2 & -5 3 & 1 array ] [ array cc 2 & -5 3 & 1 array ]= [ array cc -11 & -15 9 & -14 array ] & and A^3=A A^2= [ array cc 2 & -5 3 & 1 array ] [ array cc -11 & -15 9 & -14 array ] & = [ array cc -67 & 40 -24 & -59 array ] & aligned Use value of A^2, A^3 and I in Eq. (i), we get aligned f(A) & = [ array cc -67 & 40 -24 & -59 array ]-2 [ array cc -11 & -15 9 & -14 array ]-5 [ array ll 1 & 0 0 & 1 arra