MHT CET202416 May 2024Morning ShiftMathematicsMatricesActual
Let A = [ array ll x & 1 1 & 0 array ], x R ⁺ and A ^4= [ a _ ij ]₂ . If a ₁₁=109 , then ( A ^4 )⁻¹=
Options
- A[ array ll 109 & 33 33 & 10 array ] .
- B[ array ll 10 & 33 33 & 10 array ]
- C[ array cc 10 & 33 33 & 109 array ]
- D[ array cc 10 & -33 -33 & 109 array ]
Correct answer
D. [ array cc 10 & -33 -33 & 109 array ]
Step-by-step solution
aligned & A= [ array ll x & 1 1 & 0 array ] & A^2= [ array ll x & 1 1 & 0 array ] [ array ll x & 1 1 & 0 array ]= [ array cc x^2+1 & x x & 1 array ] & A^4=A^2 A^2 aligned aligned & = [ array cc x^2+1 & x x & 1 array ] [ array cc x^2+1 & x x & 1 array ] & = [ array ll (x^2+1 )^2+x^2 & x (x^2+1+1 ) x (x^2+1+1 ) & (x^2+1 ) array ] & = [ array cc (x^2+1 )^2+x^2 & x (x^2+2 ) x (x^2+2 ) & x^2+1 array ] array l A ^4 array & = [ a _ ij ] and a ₁₁=109 a ₁₁ & =109 & (x^2+1 )^2+x^2=109 aligned ...[Given] i.e. aligned (x^2+1 )