Answer:
- [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given the 2 by 2 matrix
[tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]
The determinant = ad - bc
For the given matrix
a = [tex]\frac{1}{2}[/tex], b = [tex]\frac{\sqrt{3} }{2}[/tex], c = [tex]\frac{\sqrt{3} }{2}[/tex], d = [tex]\frac{1}{2}[/tex] , thus
ad - bc = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] - ( [tex]\frac{\sqrt{3} }{2}[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] ) = [tex]\frac{1}{4}[/tex] - [tex]\frac{3}{4}[/tex] = - [tex]\frac{1}{2}[/tex]
