MHT CET202314 May 2023Evening ShiftMathematicsMatricesActual
If A= [ array ll 1 & -1 2 & -1 array ], B= [ array cc 1 & 1 4 & -1 array ] , then (A+B)⁻¹ is
Options
- A[ array cc -1 2 & 0 -3 2 & 1 2 array ]
- B[ array cc 1 2 & 0 3 2 & -1 2 array ]
- C[ array cc 1 2 & 0 -3 2 & 1 2 array ]
- D[ array ll 1 2 & 0 3 2 & 1 2 array ]
Correct answer
B. [ array cc 1 2 & 0 3 2 & -1 2 array ]
Step-by-step solution
aligned A+B & = [ array cc 1 & -1 2 & -1 array ]+ [ array cc 1 & 1 4 & -1 array ]= [ array cc 2 & 0 6 & -2 array ] |A+B| & = | array cc 2 & 0 6 & -2 array |=-4 0 If A & = [ array ll a & b c & d array ] and ad - bc 0, then A⁻¹ & = 1 (a d-b c) [ array cc d & -b -c & a array ] (A+B)⁻¹ & = 1 -4 [ array cc -2 & 0 -6 & 2 array ] & = [ array cc 1 2 & 0 3 2 & - 1 2 array ] aligned