Using properties of determinants porve t...

Using properties of determinants porve that, `|{:(x,x^2,1+px^3),(y,y^2,1+py^3),(z,z^2,1+pz^3):}|=(1+pxyz)(x-y)(y-z)(z-x)`

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For any scalar c prove that, |{:(x,x^2,1+cx^3),(y,y^2,1+cy^3),(z,z^2,1+cz^3):}|=(1+cxyz)(x-y)(y-z)(z-x)

By using properties of determinants , show that : {:|( x,x^(2) , yz) ,( y,y^(2) , zx ) ,( z , z^(2) , xy ) |:} =( x-y)(y-z) (z-x) (xy+yz+ zx)

If |{:(x,x^2,x^3+1),(y,y^2,y^3+1),(z,z^2,z^3+1):}|=a and x ney nez , prove that, xyz=-1.

If x,y,z are all distinct and if abs((x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^2,1+z^3)) =0,show that xyz+1=0

{:|( x,x^(2) , 1+ px^(3) ),( y,y^(2) , 1+ py^(2)),( z,z^(2) , 1+pz^(2)) |:} =( 1+pxyz ) ( x-y) ( y-z ) (z-x) , where p is any scalar .

if x+y+z=0 , then show that, |{:(1,1,1),(x,y,z),(x^3,y^3,z^3):}|=0

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The number of positive integral solutions of the equation |(x^3+1,x^2y,x^2z),(xy^2,y^3+1,y^2z),(xz^2,z^2y,z^3+1)|=11 is

If x,y,z are different and Delta = {:|( x,x^(2) , 1+x^(3)),( y,y^(3) ,1+y^(3)),( z,z^(3) ,1+z^(3)) |:} then value of delta?

Verify that x ^(3) + y ^(3) + z ^(3) - 3xyz =1/2 (x + y + z) [(x-y)^(2) + (y-z) ^(2) + (z-x) ^(2) ]

CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B

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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Show that, |{:(a^2+10,ab,ac),(ab,b^2+10,bc),(ca,bc,c^2+10):}| is divis...
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If D1 =|{:(1,1,1),(1,omega,omega^2),(1,omega^2,omega):}| and D2= |{:(1...
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Using properties of determinants porve that, |{:(x,x^2,1+px^3),(y,y^2,...
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