|{:(-a(b^2+c^2-a^2)," "2b^3,...

`|{:(-a(b^2+c^2-a^2)," "2b^3," "2c^3),(" "2a^3,-b(c^2+a^2-b^2)," "2c^3),(" "2a^3," "2b^3,-c(a^2+b^2-c^2)):}|=abc(a^2+b^2+c^2)^3`

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Explore conceptually related problems

Multiply: 2/3 abc (a^2+b^2-3c^2)

Simplify : (a - 2b + c)^3 - (a - 2b)^3 - 3c ( a - 2b +c)(a - 2b)

|{:(a,b,c),(a^2,b^2,c^2),(a^3,b^3,c^3):}|=abc(a-b)(b-c)(c-a)

Prove |{:(1,a^2+bc,a^3),(1,b^2+ca,b^3),(1,c^2+ab,c^3):}|=-(a-b)(b-c)(c-a)(a^2+b^2+c^2)

|{:(0,ab^2,ac^2),(a^2b,0,bc^2),(a^2c,cb^2,0):}|=2a^3b^3c^3

prove that, |{:(" "2a,a-b-c," "2a),(" "2b," "2b,b-c-a),(c-a-b," "2c," "2c):}|=(a+b+c)^3

Factorise : 2a^(2)+b^(2)-c^(2)+3ab+ac

If D is the mid-point of the side B C of triangle A B C and A D is perpendicular to A C , then 3b^2=a^2-c ^2 (b) 3a^2=b^2 3c^2 b^2=a^2-c^2 (d) a^2+b^2=5c^2

(a-2b)^(3)+(c-a)^(3)+(2b-c)^(3)

Using properties of determinants , prove that, |{:(a,b,c),(b,c,a),(c,a,b):}|=-(a^3+b^3+c^3-3abc) and hence show that, |{:(2bc-a^2," "c^2," "b^2),(" "c^2,2ca-b^2," "a^2),(" "b^2," "a^2,2ab-c^2):}|=(a^3+b^3+c^3-3abc)^2

CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B

|{:(logx xyz,logxy,logxz),(logyxyz,1,logyz),(logzxyz,logzy,1):}|=0
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if |{:(a+ib,c+id),(-c+id,a-ib):}|xx|{:(alpha-ibeta,gamma-idelta),(-gam...
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|{:(-a(b^2+c^2-a^2)," "2b^3," "2c^3),(" ...
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Show that |{:(x-3,x-4,x-alpha),(x-2,x-3,x-beta),(x-1,x-2,x-gamma):}|=0...
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If a, b, c, are real numbers such that |{:(b+c,c+a,a+b),(c+a,a+b,b+c...
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Show that , |{:((a^2+b^2)/c," "c," "c),(" "a,(b^2+c^2)/a," "a),(" "b,"...
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prove that , |{:(1,1+a,1+a+b),(2,3+2a,4+3a+2b),(3,6+3a,10+6a+3b):}|=1
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if f(x) =|{:(sinx,cosx,tanx),(x^3,x^2,x),(2x,1,1):}| then show that li...
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If 5 is one root of the equation |{:(x,3,7),(2,x,-2),(7,8,x):}|=0 then...
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If y =sinpx and yn is the nth derivative of y , then find the value...
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If |{:(1+ax,1+bx,1+cx),(1+a1x,1+b1x,1+c1x),(1+a2x,1+b2x,1+c2x):}|=A0+A...
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Evaluate: |{:(1,1,1),(1,omega^2,omega),(1,omega,omega^2):}| (where ome...
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If |{:(-a^2," "ab," "ac),(" "ab,-b^2," "bc),(" "ac," "bc,-c^2):}|=lamb...
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If |{:(10(c(4)),10(c(5)),11(c(m))),(11(c(6)),11(c(7)),12(c(m+2))),(12(...
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If l,m and n are real numbers such that l^2+m^2+n^2=0 , then show t...
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If f(x)= |{:(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),x(x+1)(x...
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If omega ne 1 is a cube root of unity , then find the value of |{:(...
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If alpha is a cube root of unity , then find the value of |{:(alpha...
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If f(alpha) = |{:(1,alpha,alpha^2),(alpha,alpha^2,1),(alpha^2,1,alpha)...
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Without expanding prove that, |{:(b^2c^2,bc,b+c),(c^2a^2,ca,c+a),(a^2b...
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