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Prove the following: [[-a^2,ab,ac],[ab...

Prove the following:
`[[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=4a^2b^2c^2`

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MODERN PUBLICATION-DETERMINANTS-PROBLEM
  1. Is ((1,2),(3,4)) invertible, justify ?

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  2. Evaluate the following determinants: [[1^2,2^2,3^2],[2^2,3^2,4^2],[3...

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  3. Prove the following: [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=4a^2b^...

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  4. If Aand B are square matrices of order 3, such that |A| = -1,|B| = 3 t...

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  5. For what k x+2y-3z = 2 (k+3)z = 3 (2k+1) +z = 2 is inconsisten...

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  6. The sum of two non integral roots of [[x,2,5],[3,x,3],[5,4,x]] = 0 is ...

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  7. What is the inverse of A = ((cos alpha,sin alpha),(sin alpha,-cos alph...

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  8. The value of [[1,2,3],[3,5,2],[8,14,20]] is .

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

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  10. Prove that the following. [[b+c,a,a],[b,c+a,b],[c,c,a+b]]=4ab

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  11. Solve : [[7,6,x],[2,x,2],[x,3,7]] = 0

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  12. Solve the following : [[1+x,1,1],[1,1+x,1],[1,1,1+x]]=0

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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 that the following. [[a+d,a+d+k,a+d+c],[c,c+b,c],[d,d+k,d+c]]=ab...

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  15. Prove that the following. [[1,1,1],[b+c,c+a,c+a],[b^2+c^2,c^2+a^2,a^2+...

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  16. Prove that [[b^2c^2, bc,b+c],[c^2a^2,ca,c+a],[a^2b^2,ab,a+b]] = 0

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  17. Show that: abs((1,a,a^2),(1,b,b^2),(1,c,c^2))=(a-b)(b-c)(c-a)

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  18. Show that |{:((b+c)^2,a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2):}...

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  19. Prove that [[1,a,a^2 - bc],[1,b,b^2 - ca],[1,c,c^2 - ab]]

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

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