COMEDK2018MathematicsMatrices
If A= [ array ll 1 & 2 0 & 1 array ] , then A^ n is
Options
- A[ array cc 1 & 2^ n -2 0 & 1 array ]
- B[ array cc 1 & n² 0 & 1 array ]
- C[ array cc 1 & 2 n 0 & 1 array ]
- D[ array cc 1 & n² 1 & 1 array ]
Correct answer
C. [ array cc 1 & 2 n 0 & 1 array ]
Step-by-step solution
We have, A= [ array ll 1 & 2 0 & 1 array ] aligned A² &= [ array ll 1 & 2 0 & 1 array ] [ array ll 1 & 2 0 & 1 array ] &= [ array ll 1+0 & 2+2 0+0 & 0+1 array ]= [ array ll 1 & 4 0 & 1 array ] A³ &=A² A [ array ll 1 & 4 0 & 1 array ] [ array ll 1 & 2 0 & 1 array ] &= [ array cc 1+0 & 2+4 0+0 & 0+1 array ]= [ array ll 1 & 6 0 & 1 array ] &= [ array cc 1 & 2 3 0 & 1 array ] A^ n &= [ array cc 1 & 2 n 0 & 1 array ] aligned