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Prove the following: [[a^2+1,ab,ac],[a...

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

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SHARAM PUBLICATION-DETERMINANT-EXAMPLE
  1. 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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  2. Prove that the following. [[a,b,c],[x,y,z],[p,q,r]]=[[y,b,q],[x,a,p],[...

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

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

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

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

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

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

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

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  10. Solve : |[x-a, 0, 0],[a, x-b, 0],[a, b, x-c]|=0

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  11. What is the value of the determinant |[0, 0, 2],[0, 2, 0],[2, 0 ,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. Find the value of |{:(17,58,97),(19,60,99),(18,59,98):}| without expan...

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  14. Prove that the following. [[1+a,1,1],[1,1+b,1],[1,1,1+c]] = abc(1+1/...

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  15. Evaluate the following determinants: [[0,a^2,b],[b^2,0,a^2],[a,b^2,0...

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  16. Prove that: |[a+b+2c, a, b],[c, b+c+2a, b],[c, a, c+a+2b]|=2(a+b+c)^3

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  17. Without expanding prove that |[1,a,a^(2),-bc],[1,b,b^(2),-ca],[1,c,c^(...

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  18. Prove the following : [[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]]=0

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  19. Given the equations x=cy+bz, y=az+cx and z=bx+ay where x,y and z a...

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  20. Eliminate x,y,z from a=x/y-z, b=y/z-x, c=z/x-y

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