If A= [ array cc 1 & -3 2 & k array ] and A²-4 A+10 I=A , then k=

Step-by-step solution

We have, A= [ array cc 1 & -3 2 & k array ] Now, A= [ array cc 1 & -3 2 & k array ] [ array cc 1 & -3 2 & k array ]= [ array cc 1-6 & -3-3 k 2+2 k & -6+k² array ]= [ array cc -5 & -3-3 k 2+2 k & k²-6 array ] Now, A²-4 A+10 I=A aligned [ array cc -5 & -3-3 k 2+2 k & k²-6 array ]-4 [ array cc 1 & -3 2 & k array ] &+10 [ array ll 1 & 0 0 & 1 array ]= [ array cc 1 & -3 2 & k array ] aligned aligned & [ array cc -5-4+10 & -3-3 k+12+0 2+2 k-8+0 & k²-6-4 k+10 array ]= [ array cc 1 & -3 2 & k array ] & [ array cc -1 & -3 k