MHT CET2008MathematicsMatrices
The inverse matrix of [ array lll 0 & 1 & 2 1 & 2 & 3 3 & 1 & 1 array ] is
Options
- A[ array rrr 1 2 & - 1 2 & 1 2 -4 & 3 & -1 5 2 & - 3 2 & 1 2 array ]
- B[ array rrr 1 2 & -4 & 5 2 1 & -6 & 3 1 & 2 & -1 array ]
- C1 2 [ array lll 1 & 2 & 3 3 & 2 & 1 4 & 2 & 3 array ]
- D1 2 [ array rrr 1 & -1 & -1 -8 & 6 & -2 5 & -3 & 1 array ]
Correct answer
A. [ array rrr 1 2 & - 1 2 & 1 2 -4 & 3 & -1 5 2 & - 3 2 & 1 2 array ]
Step-by-step solution
Let aligned A &= [ array lll 0 & 1 & 2 1 & 2 & 3 3 & 1 & 1 array ] aligned |A| &=0-1(1-9)+2(1-6) &=8-10=-2 0 adj (A) &= [ array rrr -1 & 1 & -1 8 & -6 & 2 -5 & 3 & -1 array ] A⁻¹ &= adj (A) |A| &= 1 -2 [ array rrr -1 & 1 & -1 8 & -6 & 2 -5 & 3 & -1 array ] &= [ array rrrr 1 / 2 & -1 / 2 & 1 / 2 -4 & 3 & -1 5 / 2 & -3 / 2 & 1 / 2 array ] aligned aligned