If A= [ array cc 1 & -2 4 & 5 array ] and f(t)=t^2-3 t+7 , then f(A)+ [ array cc 3 & 6 -12 & -9 array ] is equal to

Step-by-step solution

Given that, A= [ array cc 1 & -2 4 & 5 array ] and f(t)=t^2-3 t+7 Now, aligned A^2 & = [ array cc 1 & -2 4 & 5 array ] [ array cc 1 & -2 4 & 5 array ] & = [ array cc -7 & -12 24 & 17 array ] aligned Now, aligned & f(A)=A^2-3 A+7 & = [ array cc -7 & -12 24 & 17 array ]-3 [ array cc 1 & -2 4 & 5 array ]+7 [ array ll 1 & 0 0 & 1 array ] & = [ array cc -3 & -6 12 & 9 array ] aligned aligned f(A)+ [ array cc 3 & 6 -12 & -9 array ] & = [ array cc -3 & -6 12 & 9 array ]+ [ array cc 3 & 6 -12 & -9 array ] & = [ array ll 0