Home
Class 12
MATHS
Which of the following is a non singular...

Which of the following is a non singular matrix? (A) `[(1,a,b+c),(1,b,c+a),(1,c,a+b)]` (B) `[(1,omega, omega^2),(omega, omega^2,1),(omega^2,1,omega)]` where omega is non real and `omega^3=1` (C) `[(1^2,2^2,3^2),(2^2,3^2,4^2),(3^2,4^2,5^2)]` (D) `[(0,2,-3),(-2,0,5),(3,-5,0)]`

Promotional Banner

Similar Questions

Explore conceptually related problems

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

(2+omega+omega^2)^3+(1+omega-omega^2)^8-(1-3omega+omega^2)^4=1

Without expanding at any stage, prove that |{:(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),1,omega):}| = 0

Simplify: (1- 3omega + omega^(2)) (1 + omega- 3omega^(2))

Prove that the value of determinant |{:(1,,omega,,omega^(2)),(omega ,,omega^(2),,1),( omega^(2),, 1,,omega):}|=0 where omega is complex cube root of unity .

The determinant of the matrix A=|(1,1,1),(1,omega,omega^2),(1,omega^2,omega)|, where omega=e(2pii)/3, is

If omega is cube roots of unity, prove that {[(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega)]+[(omega,omega^2,1),(omega^2,1,omega),(omega,omega^2,1)]} [(1),(omega),(omega^2)]=[(0),(0),(0)]

If omega is cube roots of unity, prove that {[(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega)]+[(omega,omega^2,1),(omega^2,1,omega),(omega,omega^2,1)]} [(1),(omega),(omega^2)]=[(0),(0),(0)]

Prove the following (1- omega + omega^(2)) (1 + omega- omega^(2)) (1 - omega- omega^(2))= 8

If omega is an imaginary cube root of unity, then the value of |(a,b omega^(2),a omega),(b omega,c,b omega^(2)),(c omega^(2),a omega,c)| , is