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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-DETERMINANTS-All Questions
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  2. If a1b1, c1,a2b2c2a n da3b3c3 are three digit even natural numbers and...

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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,2q,3r],[1, 1, 1]|,w h e r ex ,y ,z are...

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

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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 |{:(2,,alpha+beta+gamma+delta,,alphabeta+gammadelta),(alpha...

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

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  10. The value of determinant |1 1 1^m C1^(m+1)C1^(m+2)C1^m C2^(m+1)C2^(m+2...

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  11. Solve the equation |a-x c b c b-x a b a c-x|=0w h e r ea+b+c!=0.

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

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  14. 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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  15. If |x3 6 3 6x6x3|=|2x7x7 2 7 2x|=|4 5x5x4x4 5|=0, then x is equal to 0...

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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)=|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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  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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