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

`([1,1,1],[a,b,c],[a^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)

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

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

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

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

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

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

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

If a!=b!=c such that |[a^3-1,b^3-1,c^3-1] , [a,b,c] , [a^2,b^2,c^2]|=0 then

MAHAVEER PUBLICATION-DETERMINANTS-QUESTION BANK
  1. Evaluate abs([a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c])

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  2. Prove that abs([1,1,1],[1,1+a,1],[1,1,1+b])=ab

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  3. ([1,1,1],[a,b,c],[a^2,b^2,c^2])=(a-b)(b-c)(c-a)

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  4. (iii) सारणिक का बिना विस्तार किये हुए सिद्ध करें कि |{:(a,b,c),(x,y,z)...

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  5. Prove that : Det[[x,x^2,x^3],[y,y^2,y^3],[z,z^2,z^3]]=xyz(x-y)(y-z)(z-...

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  6. Show that abs([y+z ,x,x],[y,z+x,y],[z,z,x+y])=4xyz

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  7. Show that abs([x,b,c],[x,b,y],[y,b,c])=b(x-y)(c-y)

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  8. Prove that the determinate abs([x,sintheta,costheta],[-sintheta,-x,1],...

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  9. Without expanding the determinant prove that abs([a,a^2,bc],[b,b^2,...

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  10. Solve the equation |x+a xxxx+a xxxx+a|=0, a!= 0

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  11. Find minors and cofactors of all the elements of the determinant abs([...

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  12. Solve by Cramer's rule: 3x-2y=4 6x-y=11

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  13. Solve by Cramer's rule: 3x+2y=4 8x+3y=13

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  14. Solve by Cramer's rule: 3x-2y=4 x-4y=-2

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  15. Solve by cramer's rule : 3x-5y=21 5x+y=7

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  16. Solve by cramer's rule : x+y+z=3 2x-y+3z=4 x+2y-z=2

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  17. Evaluate the determinates abs([2,3],[1,7])

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  18. Evaluate the determinates abs([-costheta,-sin theta],[sintheta,-costhe...

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  19. Evaluate the determinatesabs([3,-4,5],[1,1,-2],[2,3,1])

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  20. Evaluate the determinates abs([2,-1,-2],[0,2,-1],[3,-5,0])

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