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- If a^2+b^2+c^2=-2a n df(x)= |a+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c...
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- Consider the set A of all determinants of order 3 with entries 0 or 1 ...
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- Solve: |x^2-1x^2+2x+1 2x^2+3x+1 2x^2+x-1 2x^2+5x-3 2x^2+4x-3 6x^2-x-2 ...
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- If |x3 6 3 6x6x3|=|2x7x7 2 7 2x|=|4 5x5x4x4 5|=0, then x is equal to 0...
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- If A1B1C1 , A2B2C2 and A3B3C3 are three digit numbers, each of which ...
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- If f^(prime)(x)=|m x m x-p m x+p nn+p n-p m x+2n m x+2n+p m x+2n-p| , ...
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- If sum(n=1)^nalphan=a n^2+b n ,w h e r ea ,b are constants and alp...
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- The determinant |x p+y x y y p+z y z0x p+y y p+z|=0 if x ,y ,z
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- Using properties of determinant prove that |a+b+c-c-b-c a+b+c-a-b-a a...
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- Show that |^x Cr^x C(r+1)^x C(r+2)^y Cr^y C(r+1)^y C(r+2)^z Cr^z C(r+1...
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- If omega!=1 is a cube root of unity and x+y+z!=0, then prove tha...
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- Statement 1: If the system of equation lambdax+(b-a)y+(c-a)z=0,(a-b)x+...
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- If A , Ba n dC are the angels of a triangle, show that |-1+cos B co...
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- If alpha,beta,gamma are the angles of a triangle and system of equatio...
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- Without expanding the determinants, prove that |103 115 114 111 108 10...
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- Given a=x//(y-z), b=y//(z-x),a n dc=z//(x-y),w h e r ex , y , za n dz ...
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- Find the value of determinant |(sqrt((13))+sqrt(3),2sqrt(5),sqrt(5))sq...
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- a ,b ,c are distinct real numbers not equal to one. If a x+y+z=0,x+b y...
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- Prove that the value of the determinant |-7 5+3i2/3-4i5-3i8 4+5i2/3+4i...
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- If the system of linear equation x+y+z=6,x+2y+3c=14 ,a n d2x+5y+lambda...
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