Prove that : |{:(a^(2),b^(2)+c^(2),bc),(...

Prove that : `|{:(a^(2),b^(2)+c^(2),bc),(b^(2),c^(2)+a^(2),ca),(c^(2),a^(2)+b^(2),ab):}|=-(a-b)(b-c)(c-a)(a+b+c)(a^(2)+b^(2)+c^(2))`

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The value of determinant |{:(a^(2),a^(2)-(b-c)^(2),bc),(b^(2),b^(2)-(c-a)^(2),ca),(c^(2),c^(2)-(a-b)^(2),ab):}| is

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Prove that : |{:(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab):}|=(a-b)(b-c)(c-a)(ab+bc+ca)

Prove the identities: |{:(b^(2)+c^(2),,ab,,ac),(ab,,c^(2)+a^(2),,bc),(ca,,bc,,a^(2)+b^(2)):}|=4a^2b^2c^2

Prove: |((b+c)^2, a^2, b c) ,((c+a)^2, b^2 ,c a),( (a+b)^2, c^2, a b)|=(a-b)(b-c)(c-a)(a+b+c)(a^2+b^2+c^2) .

Prove the identities: |[a^2,a^2-(b-c)^2,b c], [b^2,b^2-(c-a)^2,c a],[ c^2,c^2-(a-b)^2,a b]|=(a-b)(b-c)(c-a)(a+b+c)(a^2+b^2+c^2)

If a, b, c are non zero complex numbers satisfying a^(2) + b^(2) + c^(2) = 0 and |(b^(2) + c^(2),ab,ac),(ab,c^(2) + a^(2),bc),(ac,bc,a^(2) + b^(2))| = k a^(2) b^(2) c^(2) , then k is equal to

Prove that : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Prove that : |{:(a^(2),bc,ac+c^(2)),(a^(2)+ab,b^(2),ac),(ab,b^(2)+bc,c^(2)):}|=4a^(2)b^(2)c^(2)

Prove that Delta = |{:(1,,1,,1),(a,,b,,c),(bc+a^(2),,ac+b^(2),,ab+c^(2)):}| = 2(a-b)(b-c)(c-a)

NAGEEN PRAKASHAN ENGLISH-DETERMINANTS-Exercise 4b

Prove that : Det[[x,x^2,x^3],[y,y^2,y^3],[z,z^2,z^3]]=xyz(x-y)(y-z)(z-...
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Prove that : |{:(1,x,x^(3)),(1,y,y^(3)),(1,z,z^(3)):}|=(x-y)(y-z)(z-x)...
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Prove that : |{:(x+a,x,x),(x,x+a,x),(x,x,x+a):}|=a^(2)(3x+a)
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Prove that : |{:(x+a,b,c),(a,x+b,c),(a,b,x+c):}|=x^(2)(x+a+b+c)
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Prove that : |{:(x-y-z ,2x, 2x),(2y,y-z-x,2y),(2z,2z,z-x-y):}|=(x+y+z)...
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Prove that : |{:(x+y+2z,x,y),(z,y+z+2x,y),(z,x,x+z+2y):}|=2(x+y+z)^(3)
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Using the properties of determinants, prove that |{:((y+z)^(2)," "x...
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Prove that : |{:(a+b,b,c),(b+c,c,a),(c+a,a,b):}|=3 abc-a^(3)-b^(3)-c^(...
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Prove that : |{:(a^(2),b^(2)+c^(2),bc),(b^(2),c^(2)+a^(2),ca),(c^(2),a...
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Prove that : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Pr...
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Prove that : |{:(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab):}|=(a-b)(b-c)(c...
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Prove that : |{:(0,a-b,a-c),(b-a,0,b-c),(c-a,c-b,0):}|=0
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|[x,-6,-1],[2,-3x,x-3],[-3,2x,x+2]|=0
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Solve the equation |{:(x+a,x+b,x+c),(x+b,x+c,x+a),(x+c,x+a,x+b):}|=0
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One root of the equation |(3x-8, 3, 3),(3,3x-8, 3),(3,3,3x-8)|=0 is ...
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If 2s=a+b+c and A=|[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[(s-c)^...
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If the sides of a DeltaABC are a, b, c and |{:(a^(2),b^(2),c^(2)),((a+...
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If the pth, qth and rth terms of a G.P, are x,y and z repectively, the...
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Prove that : |{:(1,1,1),(x,y,z),(x^(3),y^(3),z^(3)):}|=(x-y)(y-z)(z-x)...
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Prove that : |{:(y+z,x,y),(z+x,z,x),(x+y,y,z):}|=(x+y+z)(x-z)^(2)
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