JEE Main2014MathematicsMatricesActual
Let A be a 3 3 matrix such that A [ array lll 1 & 2 & 3 0 & 2 & 3 0 & 1 & 1 array ]= [ array lll 0 & 0 & 1 1 & 0 & 0 0 & 1 & 0 array ] Then A ⁻¹ is:
Options
- A[ array lll 3 & 1 & 2 3 & 0 & 2 1 & 0 & 1 array ]
- B[ array lll 3 & 2 & 1 3 & 2 & 0 1 & 1 & 0 array ]
- C[ array lll 0 & 1 & 3 0 & 2 & 3 1 & 1 & 1 array ]
- D[ array lll 1 & 2 & 3 0 & 1 & 1 0 & 2 & 3 array ]
Correct answer
A. [ array lll 3 & 1 & 2 3 & 0 & 2 1 & 0 & 1 array ]
Step-by-step solution
Given A [ array lll 1 & 2 & 3 0 & 2 & 3 0 & 1 & 1 array ]= [ array lll 0 & 0 & 1 1 & 0 & 0 0 & 1 & 0 array ] Applying C ₁ C ₃ A [ array lll 3 & 2 & 1 3 & 2 & 0 1 & 1 & 0 array ]= [ array lll 1 & 0 & 0 0 & 0 & 1 0 & 1 & 0 array ] Again Applying C ₂ C ₃ A [ array lll 3 & 1 & 2 3 & 0 & 2 1 & 0 & 1 array ]= [ array lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ] pre-multiplying both sides by A ⁻¹ aligned & A ⁻¹ ~A [ array lll 3 & 1 & 2 3 & 0 & 2 1 & 0 & 1 array ]= A ⁻¹ [ array lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ] & I [