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Evaluate the following determinants: [...

Evaluate the following determinants:
`[[a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c]]`

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Evaluate the following determinants: [[a-b,b-c,c-a],[x-y,y-z,z-x],[p-q,q-r,r-p]]

Find the value of |[a-b,b+c,a],[b-a,c+a,b],[c-a,a+b,c]| ?

Without expanding,show that the following determinant vanishes. abs((b^2c^2,bc,b+c),(c^2a^2,ca,c+a),(a^2b^2,ab,a+b))

Without expanding,show that the following determinant vanishes. abs ((1,bc,a(b+c)),(1,ca,b(c+a)),(1,ab,c(a+b)))

Prove the following: [[a+b+c,-c,-b],[-c,a+b+c,-a],[-b,-a,a+b+c]] =2(b+c)(c+a)(a+b)

Prove that the following. [[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

Prove the following: [[a,b,c],[b,c,a],[c,a,b]]=3abc-a^3-b^3-c^3

Show that abs{:(b-c,c-a,a-b),(c-a,a-b,b-c),(a-b,b-c,c-a):}=0.

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SHARAM PUBLICATION-DETERMINANT-EXAMPLE
  1. what is value of: |[cosec^2theta,cot^2theta,1],[cot^2theta,cosec^2thet...

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  2. Evaluate the following determinants. [[1,x,y],[0,sinx,siny],[0,cosx,c...

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  3. Evaluate the following determinants: [[a-b,b-c,c-a],[b-c,c-a,a-b],[c...

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  4. Write the value of |[2,3,4],[5,6,8],[6x,9x,12x]|

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  5. What is the value of : |[4,a,b+c ],[4,b,c+a],[4,c,a+b]|

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  6. What is the value of the determinant |[102,18,36],[1,3,4],[17,3,6]|?

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  7. Solve the following : [[x+1,omega,omega^2],[omega,x+omega^2,1],[omega^...

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  8. Solve the following : [[0,x-a,x-b],[x+a,0,x-c],[x+b,x+c,0]]=0

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  9. Prove that the following. [[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=...

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  10. Prove without expanding that |[bc,a,a^2],[ca,b,b^2],[ab,c,c^2]|=|[1,a^...

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  11. Factorise the determinant |[x^3-a^3,x^2,x],[b^2-a^3,b^2,b],[c^3-a^3,c^...

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  12. Show that (a+1) is a factor of abs([(a+1),2,3],[1,a+1,3],[3,-6,a+1])

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  13. Prove that the following. [[a,b,c],[x,y,z],[p,q,r]]=[[y,b,q],[x,a,p],[...

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  14. Prove the following: [[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]] =1+...

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  15. Solve for x, |{:(15-2x,11,10),(11-3x,17,16),(7-x,14,13):}|=0

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  16. What is the value of |[i^(103), 3 ,i^(101)],[i^(56), 5, i^(54)],[i^(23...

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  17. Without expanding find the value of the deteminant |[3, 6, 9],[-2, 4 ,...

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  18. Prove that:|[1, a ,a^2],[a^2, 1 ,a],[a, a^2, 1]| is a perfect square.

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  19. Without expanding prove that: |[12, 2, 4, -5, 1],[-8, 1, -5, 2, -1],[6...

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  20. Prove that: |[1, 1, 1],[a, b, c],[a^2, b^2, c^2]|=(a-b)(b-c)(c-a)

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