Question
Let A= [ array ccc 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 array ] and 10 B= [ array ccc 4 & 2 & 2 \\ -5 & 0 & \\ 1 & -2 & 3 array ] If B is the inverse of A, then the value of is
BITSAT
Mathematics
Matrices
2022
BITSAT 2022
BITSAT Mathematics Question (2022) — Solution
Options
- A. 4
- B. 3
- C. -4
- D. 5
Answer
D. 5
Step-by-step solution
A= [ array ccc 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 array ] |A|= [ array ccc 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 array ] =1(1+3)+1(2+3)+1(2-1)=4+5+1=10 Adj A= [ array ccc 4 & -5 & 1 \\ 2 & 0 & -2 \\ 2 & 5 & 3 array ]^T= [ array ccc 4 & 2 & 2 \\ -5 & 0 & 5 \\ 1 & -2 & 3 array ] B=A^ -1 = 1 10 [ array ccc 4 & 2 & 2 \\ -5 & 0 & 5 \\ 1 & -2 & 3 array ] [ A^ -1 = 1 |A| Adj A ] 10 B= [ array ccc 4 & 2 & 2 \\ -5 & 0 & 5 \\ 1 & -2 & 3 array ] Hence, =5
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