AP EAMCET202017 Sep 2020Evening ShiftMathematicsMatricesActual
For (M= [ array ll 3 & -4 1 & -1 array ] ) and for any (n N ) the matrix (M^ n+1 -M^n= )
Options
- A( [ array cc 2 & 4 1 & -2 array ] )
- B( [ array ll 2 & -4 1 & -2 array ] )
- C( [ array cc 2 & -4 1 & 2 array ] )
- D( [ array ll 2 & 4 1 & 2 array ] )
Correct answer
B. ( [ array ll 2 & -4 1 & -2 array ] )
Step-by-step solution
( aligned M & = [ array ll 3 & -4 1 & -1 array ] M^2 & = [ array ll 3 & -4 1 & -1 array ] [ array ll 3 & -4 1 & -1 array ] & = [ array ll 9-4 & -12+4 3-1 & -4+1 array ]= [ array ll 5 & -8 2 & -3 array ] M^2-M & = [ array ll 5 & -8 2 & -3 array ]- [ array ll 3 & -4 1 & -1 array ]= [ array ll 2 & -4 1 & -2 array ] aligned ) So; (M^ n+1 -M=M^2-M= [ array ll 2 & -4 1 & -2 array ] )