NDA2017MathematicsMatricesActual
If a, b, c are non-zero real numbers, then the inverse of the matrix A= [ array lll a & 0 & 0 0 & ~b & 0 0 & 0 & c array ] is equal to
Options
- A[ array lll a ⁻¹ & 0 & 0 0 & ~b ⁻¹ & 0 0 & 0 & c ⁻¹ array ]
- B1 abc [ array lll a ⁻¹ & 0 & 0 0 & ~b ⁻¹ & 0 0 & 0 & c ⁻¹ array ]
- C1 abc [ array lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ]
- D1 abc [ array lll a & 0 & 0 0 & ~b & 0 0 & 0 & c array ]
Correct answer
A. [ array lll a ⁻¹ & 0 & 0 0 & ~b ⁻¹ & 0 0 & 0 & c ⁻¹ array ]
Step-by-step solution
A = [ array lll a & 0 & 0 0 & ~b & 0 0 & 0 & c array ] A ⁻¹= [ array ccc 1 a & 0 & 0 0 & 1 ~b & 0 0 & 0 & 1 c array ]= [ array ccc a ⁻¹ & 0 & 0 0 & ~b ⁻¹ & 0 0 & 0 & c ⁻¹ array ]