If A= [ array rr -8 & 5 2 & 4 array ] satisfies the equation x^2+4 x-p=0 , then p is equal to

Step-by-step solution

aligned & = [ array rr 64+10 & -40+20 -16+8 & 10+16 array ] & = [ array ll 74 & -20 -8 & 26 array ] & 4 A= [ array rr -32 & 20 8 & 16 array ] & -p l= [ array cc -p & 0 0 & -p array ] & aligned Since, the matrix A satisfies the equation aligned & x^2+4 x-p=0, then & A^2+4 A-p l=0 & [ array rr 74 & -20 -8 & 26 array ]+ [ array rr -32 & 20 8 & 16 array ]+ [ array cc -p & 0 0 & -p array ] & [ array ll 74-32-p & -20+20+0 [ array cc 0 & 0 -8+8+0 & 26+16-p array ]= [ array ll 0 & 0 array ] 0 & 0 array ] & [ array cc 42-p