AP EAMCET202317 May 2023Evening ShiftMathematicsMatricesActual
If A= [ array lll 1 & 0 & 1 0 & 1 & 1 0 & 1 & 0 array ] , then A⁻¹=
Options
- AA -2 ~A ^2
- B2 ~A - A ^2
- C2 ~A ^2+ A
- D2 ~A + A ^2
Correct answer
B. 2 ~A - A ^2
Step-by-step solution
A= [ array lll 1 & 0 & 1 0 & 1 & 1 0 & 1 & 0 array ]|A- I|=0 | array ccc 1- & 0 & 1 0 & 1- & 1 0 & 1 & - array |=0 aligned & (1- )[-(1- ) -1]=0 & ^3-2 ^2+1=0 aligned Every matrix satispfies its characterstic equation. A^3-2 A^2+I=0 Multiplying by A ⁻¹ in both sides: aligned & A ^2-2 ~A + A ⁻¹=0 & A ⁻¹=2 ~A - A ^2 aligned