|{:(alpha,beta,gamma),(alpha^2,beta^2,ga...

` |{:(alpha,beta,gamma),(alpha^2,beta^2,gamma^2),(beta+gamma,gamma+alpha,alpha+beta):}|`

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The correct Answer is:

`(alpha-beta)(beta-gamma)(gamma-alpha)(alpha+beta+gamma)`

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CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B

Let A=|{:(" "1," "sin theta,1),(-sin theta," "1,sintheta),(-1,-sinth...
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Let A be a square matrix of order 3xx3, then |KA| is equal to
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|{:(alpha,beta,gamma),(alpha^2,beta^2,gamma^2),(beta+gamma,gamma+alpha...
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|{:(x,a,b),(a,x,b),(a,b,x):}|
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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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|{:(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^3),(1,beta,beta^3),(1,gamma,gamma^3):}|=(alpha-beta)...
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