A) \[\sqrt{3}\]
B) \[-2\sqrt{3}\]
C) \[-\sqrt{3}\]
D) \[2\sqrt{3}\]
Correct Answer: D
Solution :
\[det\left( A \right)=2\left( 2{{b}^{2}}+2-{{b}^{2}} \right)-b\left( 2b-b \right)\] \[+1\left( {{b}^{2}}-{{b}^{2}}-1 \right)\] \[=\,\,2\left( {{b}^{2}}+2 \right)-{{b}^{2}}-1\] \[=\text{ }{{b}^{2}}+3\] \[\frac{\det (A)}{b}\,\,=\,\,\frac{{{b}^{2}}+3}{b}\,\,=b+\frac{3}{b}\] Minimum value \[=\,\,2\sqrt{3}\]
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