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If =|[a b c, b^2c,c^2b],[ a b c,c^2a, c ...

If `=|[a b c, b^2c,c^2b],[ a b c,c^2a, c a^2],[a b c, a^2b,b^2a]|=0,(a ,b ,c in R)` and are all different and nonzero), then prove that `a+b+c=0.`

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CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. The value of the determinant of n^(t h) order, being given by |[x, 1, ...

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  2. Prove that a!=0,|[x+a, x,x],[x,x+a,x],[x,x,x+a^2]|=0 represents a stra...

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  3. If =|[a b c, b^2c,c^2b],[ a b c,c^2a, c a^2],[a b c, a^2b,b^2a]|=0,(a ...

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  4. The value of |[yz, z x,x y],[ p,2p,3r],[1, 1, 1]|,w h e r ex ,y ,z ar...

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  5. Show that the determinant |a^2+b^2+c^2b c+c a+a bb c+c a+a bb c+c a+a ...

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  6. If x!=0,y!=0,z!=0 and |[1+x,1,1],[1+y,1+2y,1],[1+z,1+z,1+3z]|=0, then ...

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  7. If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, th...

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  8. Prove that |2alpha+beta+gamma+deltaalphabeta+gammadelta alpha+beta+g...

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  9. Solve for x , |[x,-6,-1], [ 2,-3x,x-3], [-3, 2x, x+2]|=0.

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  10. The value of the determinant |{:(1,,1,,1),(.^(m)C(1),,.^(m+1)C(1),...

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  11. Solve the equation |[a-x, c, b], [ c, b-x, a], [b, a, c-x]|=0 where a...

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  12. If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c...

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  13. Consider the set A of all determinants of order 3 with entries 0 or 1 ...

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  14. Solve: |[x^2-1, x^2+2x+1, 2x^2+3x+1], [2x^2+x-1, 2x^2+5x-3, 2x^2+4x-3...

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  15. If |[x,3, 6],[ 3, 6,x],[6,x,3]|=|[2,x,7],[x,7, 2],[ 7, 2,x]|=|[4, 5,x]...

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  16. If A1B1C1 , A2B2C2 and A3B3C3 are three digit numbers, each of which ...

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  17. If f^(prime)(x)=|[mx, mx-p, m x+p], [n, n+p, n-p], [mx+2n, m x+2n+p, m...

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  18. If sum(n=1)^nalphan=a n^2+b n ,w h e r ea ,b are constants and alp...

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  19. 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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  20. Using properties of determinant prove that |a+b+c-c-b-c a+b+c-a-b-a a...

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