NDA2024MathematicsMatricesActual
Paragraph: Let A = [ array lll 3 & -3 & 4 2 & -3 & 4 0 & -1 & 1 array ] Question: What is A⁻¹ equal to?
Options
- A[ array ccc 1 & -1 & 0 -2 & 3 & -4 -2 & 3 & -3 array ]
- B[ array ccc 1 2 & -1 2 & 0 -1 & 3 2 & -2 -1 & 3 2 & -3 2 array ]
- C[ array ccc 2 & -2 & 0 -4 & 6 & -8 -4 & 6 & -6 array ]
- D[ array ccc 1 5 & -1 5 & 0 -2 5 & 3 5 & -4 5 -2 5 & 3 5 & -3 5 array ]
Correct answer
A. [ array ccc 1 & -1 & 0 -2 & 3 & -4 -2 & 3 & -3 array ]
Step-by-step solution
We have : A= [ array lll 3 & -3 & 4 2 & -3 & 4 0 & -1 & 1 array ] So, Determinant aligned & |A|=3(-3+4)-2(-3+4)+0=3-2=1 & A( adj A)=|A| I=1 . I=I . aligned Now, adj ( A )= [ array ccc 1 & -1 & 0 -2 & 3 & -4 -2 & 3 & -3 array ] So, aligned & A ⁻¹= 1 | ~A | ( Adj ( A ))= 1 1 [ array ccc 1 & -1 & 0 -2 & 3 & -4 -2 & 3 & -3 array ] & A ⁻¹= [ array ccc 1 & -1 & 0 -2 & 3 & -4 -2 & 3 & -3 array ] aligned