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Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2...

Prove that `|(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)`

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Show that |[1,a,a^2],[1,b,b^2],[1,c,c^2]|=(a-b)(b-c)(c-a)

Value of |(1,a,a^2),(1,b,b^2),(1,c,c^2)| is (A) (a-b)(b-c)(c-a) (B) (a^2-b^2)(b^2-c^2)(c^2-a^2) (C) (a-b+c)(b-c+a)(c+a-b) (D) none of these

1,1,1a,b,ca^(2),b^(2),c^(2)]|=(a-b)(b-c)(c-a)

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([1,1,1a,b,ca^(2),b^(2),c^(2)])=(a-b)(b-c)(c-a)

Prove that |{:(1, a, a^(2)-bc),(1, b, b^(2)-ca), (1, c, c^(2)-ab):}|=0

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Prove that: |1a a^2-b c1bb^2-c a1cc^2-a b|=0

Without expanding the determinant , prove that |{:(a, a^(2),bc),(b,b^(2),ca),(c,c^(2),ab):}|=|{:(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3)):}|

Prove that =|1 1 1a b c b c+a^2a c+b^2a b+c^2|=2(a-b)(b-c)(c-a)

MODERN PUBLICATION-DETERMINANTS-Exercise 4(b) (LONG ANSWER TYPE QUESTIONS (II))
  1. Prove, using properties of determinants: |y+k y y y y+k y y y y+k|=k^...

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  2. for x,x,z gt 0 Prove that |{:(1,,log(x)y,,log(x)z),(log(y)x,,1,,log(y)...

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  3. Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)

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  4. Prove that |(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,c)|=(a+b+c)(a^(2)+b^(2)...

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  5. Prove the following : |{:(1,a,a),(a,1,a),(a,a,1):}|=(2a+1)(1-a)^(2)

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  6. Prove that : |{:(1,x,x^(3)),(1,y,y^(3)),(1,z,z^(3)):}|

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  7. Prove the following : |{:(1,1,1),(a,b,c),(bc,ca,ab):}|=(a-b)(b-c)(c-...

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  8. |[1,a, bc] ,[1, b, ca], [1, c, ab]| =(a-b)(b-c)(c-a)

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  9. Prove the following : |{:(bc,a,1),(ca,b,1),(ab,c,1):}|=(a-b)(b-c)(a-...

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  10. Prove the following : |{:(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab):}|=|...

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  11. Prove the following : |{:(a^(2),a,b+c),(b^(2),b,c+a),(c^(2),c,a+b):}...

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  12. Prove that |{:(a,b,c),(a^(2),b^(2),c^(2)),(b+c,c+a,a+b):}|=(a-b)(b-c)(...

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  13. Prove the following : |{:(x,x^(2),y+z),(y,y^(2),z+x),(z,z^(2),x+y):}...

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  14. Prove the following : |{:(alpha,alpha^(2),beta+gamma),(beta,beta^(2)...

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  15. |[a,b,c],[a-b,b-c,c-a],[b+c,c+a,a+b]|=a^3+b^3+c^3-3abc

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  16. Evaluate the following: |[a^2+2a, 2a+1, 1],[2a+1, a+2, 1],[3,3,1]|

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  17. Given : a^(2)+b^(2)+c^(2) =0 Prove the following : |{:(b^(2)+c^(2...

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  18. |[1+a^2-b^2,2ab,-2b],[2ab,1-a^2+b^2,2a],[2b,-2a,1-a^2-b^2]|=(1+a^2+b^2...

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  19. Prove the following : |{:(x,y,z),(x^(2),y^(2),z^(2)),(x^(3),y^(3),z^...

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  20. [[x, x^2, yz],[y, y^2, zx],[z, z^2, xy]]=(x-y)(y-z)(z-x)(xy+yz+zx)

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