Find the values of the following determi...

Find the values of the following determinants :
(i) `|{:(12,3,4),(16,5,0),(21,-1,2):}|`
(ii) `|{:(256,240,219),(240,225,198),(219,198,181):}|`
(iii) `|{:(17,19,24),(6,8,13),(-1,1,6):}|`
(iv) `|{:(67,19,21),(39,13,14),(81,24,26):}|`
(v) `|{:(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),omega,1):}|" where "omega "is a cube root of unity".`
(iv) `|{:(1,x,y),(0,(2pi)/5,sin(pi)/10),(0,sin((2pi)/5),cos(pi)/10):}|`

Text Solution

Verified by Experts

The correct Answer is:

(i) -460
(ii) 0
(iii) 0
(iv) -43
(v) 0
(vi) 0

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Evaluate |(1,omega,omega^2),(omega,omega^2,1),(omega^2,omega,omega)| where omega is cube root of unity.

|[1,omega,omega^2] , [omega, omega^2,1] , [omega^2,1,omega]|=0

Knowledge Check

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 ?

A

A) 0

B

B) 1

C

C) 2

D

D) 3

The value of the determinant |(1,omega^(3),omega^(5)),(omega^(3),1,omega^(4)),(omega^(5),omega^(4),1)| , where omega is an imaginary cube root of unity, is

A

`(1 - omega)^(2)`

B

3

C

`-3`

D

none of these

For what value of x, will |(x+omega^2,omega,1),(omega,omega^2,1=x),(1,x+omega,omega^2)| =0

A

x = 0

B

x = 1

C

x = 2

D

x = - 1

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