|{:(1,omega,omega^2),(omega,omega^2,1),(...

`|{:(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega):}|=0` where `omega` is an imaginary cube root of unity.

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Evalute: |{:(1,omega^3,omega^2),(omega^3,1,omega),(omega^2,omega,1):}| , where omega is an imaginary cube root of unity .

Evaluate abs((1,omega,omega^2),(omega^2,1,omega),(omega^2,omega,1)) were omega is an imaginary cube root of unity.

(b) answer any one of the foll.: (i) prove without expanding |[1,omega,omega ^2],[omega ,omega ^2 ,1],[omega ^2,1, omega]|=0 wher w is an imaginary cube root of unity.

Evaluate: |{:(1,1,1),(1,omega^2,omega),(1,omega,omega^2):}| (where omega is an imaginary cube root of unity ).

The value of (1-omega+omega^(2))^(5)+(1+omega-omega^(2))^(5) , where omega and omega^(2) are the complex cube roots of unity is

If x=omega-omega^2-2 then , the value of x^4+3x^3+2x^2-11x-6 is (where omega is a imaginary cube root of unity)

If 1, omega, omega^(2) are the cube roots of unity, then the value of |(1,omega^(n),omega^(2n)),(omega^(n),omega^(2n),1),(omega^(2n),1,omega^(n))| is equal to -

The condition satisfied by omega the imaginary ,cube root of unity is

If p lt 0 and alpha, beta, gamma are cube roots of p then for any a,b and c show that (aalpha+b beta + cgamma)/(a beta+bgamma +calpha)=omega^(2) where omega is an imaginary cube root of 1.

the area of the triangle formed by 1, omega, omega^2 where omega be the cube root of unity is

CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B

|{:(2,3,4),(3,4,5),(4,5,6):}|=0
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|{:(a,b,c),(x,y,z),(p,q,r):}|=|{:(x,y,z),(p,q,r),(a,b,c):}|=|{:(y,b,q)...
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|{:(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega):}|=0 where om...
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|{:(b+c,a,1),(c+a,b,1),(a+b,c,1):}|=0
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|{:(a-b,1,a),(b-c,1,b),(c-a,1,c):}|=|{:(a,1,b),(b,1,c),(c,1,a):}|
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|{:(a+1,a+4,a+2),(a+2,a+5,a+4),(a+3,a+6,a+6):}|=0
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|{:(" "0," "a,b),(-a," "0,c),(-b,-c,0):}|
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|{:(9,9,12),(1,-3,-4),(1,9,12):}|=0
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|{:(a,a^2,bc),(b,b^2,ca),(c,c^2,ab):}|=|{:(1,a^2,a^3),(1,b^2,b^3),(1,c...
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|{:(441,442,443),(445,446,447),(449,450,451):}|=0
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Prove |{:(cos(x-a),cos(x+a),cosx),(sin(x+a),sin(x-a),sinx),(cosa tan x...
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|{:(101,103,105),(104,105,106),(107,108,109):}|=0
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|{:(5^2,5^3,5^4),(5^3,5^4,5^5),(5^4,5^6,5^7):}|=0
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|{:(1,alpha,alpha^2),(1,beta,beta^2),(1,gamma,gamma^2):}|=(alpha-beta)...
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|{:(1,1,1),(a,b,c),(bc,ca,ab):}|=(a-b)(b-c)(c-a)
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|{:(1,alpha,alpha^3),(1,beta,beta^3),(1,gamma,gamma^3):}|=(alpha-beta)...
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|{:(a+b+2c," "a," "b),(" "c,b+c+2a," "b),(" "c,...
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|{:(1,1,1),(a^2,b^2,c^2),(a^3,b^3,c^3):}|=(b-c)(c-a)(a-b)(bc+ca+ab)
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|{:(a,b,c),(a^2,b^2,c^2),(a^3,b^3,c^3):}|=abc(a-b)(b-c)(c-a)
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|{:(a,b,c),(a^2,b^2,c^2),(b+c,c+a,a+b):}|=(a-b)(b-c)(c-a)(a+b+c)
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