|[1,0,w^(6)],[omega^(6),omega^(3),omega^(7)],[omega^(8),omega^(7),(1)/(6)]|=

If omega is the cube root of unity then find the value of |[1,omega^(6),omega^(8)],[omega^(6),omega^(3),omega^(7)],[omega^(8),omega^(7),1]|

Solve: /_\ = |[omega^(3),omega^(4),omega^(5)],[omega^(6),omega^(8),omega^(2)],[omega^(7),omega^(9),omega]|

If omega is the cube root of unity,prove that det[[omega^(6),omega^(3),omega^(8)omega^(8),omega^(7),1]]=3

(1-omega+omega^(2))^(6)+(1-omega^(2)+omega)^(6)

(1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8))(1-omega^(8)+omega^(16))

What is the value of |(1,omega,2 omega^(2)),(2,2omega^(2),4 omega^(3)),(3,3 omega^(3),6 omega^(4))| , where omega is the cube root of the unity ?

Which of the following cannot be valid assignmentof probabilities for outcomes of sample space S={omega_(1),omega_(2),omega_(3),omega_(4),omega_(5),omega_(6),omega_(7)} ? Assignement omega_(1),omega_(2),omega_(3),omega_(4),omega_(5),omega_(6),omega^(7) a. 0.1,0.01,0.05,0.03,0.01,0.3,0.6 b. 1/7,1/7,1/7,1/7,1/7,1/7,1/7 c. 0.1,0.2,0.3,0.4,0.5,0.6,0.7 d. -0.1,0.2,0.3,0.4,-0.2,0.1,0.3 e. 1/14,2/14,3/14,4/14,5/14,6/14,15/14

(1-omega+omega^(2))^(7)+(1+omega-omega^(2))^(7)