Question

If ${\displaystyle A^{-1}=\frac{1}{3}\left[\begin{array}{ccc}1& 4& -2\\ -2& -5& 4\\ 1& -2& 1\end{array}\right]}$ and | A | = 3, then (adj. A) = _______

विकल्प

• ${\displaystyle \frac{1}{9}\left[\begin{array}{ccc}1& 4& -2\\ -2& -5& 4\\ 1& -2& 1\end{array}\right]}$

• ${\displaystyle \left[\begin{array}{ccc}1& -2& 1\\ 4& -5& -2\\ -2& 4& 1\end{array}\right]}$

• ${\displaystyle \left[\begin{array}{ccc}1& 4& -2\\ -2& -5& 4\\ 1& -2& 1\end{array}\right]}$

• ${\displaystyle \left[\begin{array}{ccc}-1& -4& 2\\ 2& 5& -4\\ 1& -2& 1\end{array}\right]}$

Answer 1

(C)

${\displaystyle A^{-1}=\frac{1}{\left|A\right|}\left(adjA\right)}$

${\displaystyle \frac{1}{3}\left[\begin{array}{ccc}1& 4& -2\\ -2& -5& 4\\ 1& -2& 1\end{array}\right]=\frac{1}{3}\left(adjA\right)}$

${\displaystyle \left(adjA\right)=\left[\begin{array}{ccc}1& 4& -2\\ -2& -5& 4\\ 1& -2& 1\end{array}\right]}$