Determinants Matrices Question 87
Question: If $ A= \begin{bmatrix} 3 & 2 \\ 1 & 4 \\ \end{bmatrix} , $ then what is A (adj A) equal to ?
Options:
A) $ \begin{bmatrix} 0 & 10 \\ 10 & 0 \\ \end{bmatrix} $
B) $ \begin{bmatrix} 10 & 0 \\ 0 & 10 \\ \end{bmatrix} $
C) $ \begin{bmatrix} 1 & 10 \\ 10 & 1 \\ \end{bmatrix} $
D) $ \begin{bmatrix} 10 & 1 \\ 1 & 10 \\ \end{bmatrix} $
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ LetA= \begin{bmatrix} 3 & 2 \\ 1 & 4 \\ \end{bmatrix} $ We have If A is a square matric of order n then $ A(adjA)=| A |.I _{n} $ Here, $ n=2 $
$ \therefore A(adjA)=I_2| A | $
$ = \begin{bmatrix} 1 & 0 \\ 0 & 1 \\ \end{bmatrix} \begin{vmatrix} 3 & 2 \\ 1 & 4 \\ \end{vmatrix}= \begin{bmatrix} 1 & 0 \\ 0 & 1 \\ \end{bmatrix} (12-2)=10 \begin{bmatrix} 1 & 0 \\ 0 & 1 \\ \end{bmatrix} $
$ = \begin{bmatrix} 10 & 0 \\ 0 & 10 \\ \end{bmatrix} $
BETA
