Determinants Matrices Question 97
Question: If $ A= \begin{bmatrix} 0 & 1 & 3 \\ 1 & 2 & 3 \\ 3 & a & 1 \\ \end{bmatrix} $ and $ {A^{-1}}= \begin{bmatrix} 1/2 & -1/2 & 1/2 \\ -4 & 3 & c \\ 5/2 & -3/2 & 1/2 \\ \end{bmatrix} $ Then the value of $ a+c $ is equal to
Options:
A) 1
B) 0
C) 2
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] We have, $ I=A{A^{-1}} $
$ =\frac{1}{2} \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1 \\ \end{bmatrix} \begin{bmatrix} 1 & -1 & 1 \\ -8 & 6 & 2c \\ 5 & -3 & 1 \\ \end{bmatrix} $
$ = \begin{bmatrix} 1 & 0 & c+1 \\ 0 & 1 & 2(c+1) \\ 4(1-a) & 3(a-1) & 2+ac \\ \end{bmatrix} = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} $ Comparing the elements we get $ c+1=0\Rightarrow c=-1 $ and $ a-1=0\Rightarrow a=1 $
BETA
