Determinants Matrices Question 165
Question: If $ {\Delta_1}= \begin{vmatrix} x & b & b \\ a & x & b \\ a & a & x \\ \end{vmatrix} $ and $ {\Delta_2}= \begin{vmatrix} x & b \\ a & x \\ \end{vmatrix} $ are the given determinants, then
Options:
A) $ {\Delta_1}=3{{({\Delta_2})}^{2}} $
B) $ \frac{d}{dx}({\Delta_1})=3({\Delta_2}) $
C) $ \frac{d}{dx}({\Delta_1})=3{{({\Delta_2})}^{2}} $
D) $ {\Delta_1}=3{\Delta_2}^{3/2} $
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ {\Delta_1}=x(x^{2}-ab)-b(ax-ab)+b(a^{2}-ax) $
$ =x^{3}-3abx+ab^{2}+a^{2}b $
$ \frac{d}{dx}({\Delta_1})=3x^{2}-3ab=3(x^{2}-ab)=3{\Delta_2} $
BETA
