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Prove that the following. [[b^2+c^2,ab,a...

Prove that the following. `[[b^2+c^2,ab,ac],[ab,c^2+a^2,bc],[ca,cb,a^2+b^2]]=4a^2b^2c^2`

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USHA PUBLICATION-MATRICES DETERMINANTS PROBABILITY -EXERCISE
  1. If A=[[1,2,],[3,4,]],B=[[-2,3,],[-1,2,]],show that (A+B)^T=A^T+B^T.

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  2. If A=[[2,0,3,],[3,4,5,]],B=[[3,-1,2,],[0,2,3,]]and c=[[2,-3,0,],[1,4,5...

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  3. If A=[[1,2,],[3,4,]],B=[[-2,3,],[-1,2,]],show that (A+B)^T=A^T+B^T.

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  4. If A=[[2,0,3,],[3,4,5,]],B=[[3,-1,2,],[0,2,3,]]and c=[[2,-3,0,],[1,4,5...

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  5. Find the matrix A if A^2=[[17,8,],[8,17,]].

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  6. Verify that (AB)^-1=B^-1A^-1 if A=[[2,3,],[1,-1,]],B=[[0,1,],[3,1,]]

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  7. Verify that (AB)^-1=B^-1A^-1 if A=[[1,2,3,],[4,5,6,],[7,8,9,]],B=[[1,2...

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  8. If A=[[1,-1,1,],[2,-1,0,],[1,0,0,]],then show that A^2=A^-1.

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  9. If A=[{:(3,1),(-1,2):}] then prove that A^(2)-5A+7I=O

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  10. Show that the matrix A=[[2,3,],[1,2,]]satisfies the equation A^2-4A+I=...

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  11. If A=[{:(costheta,sintheta),(-sintheta,costheta):}], then prove that ...

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  12. Express the matrix A=[[4,2,-3],[1,3,-6],[-5,0,-7]] as the sum of symme...

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  13. Examining consistency and solvability, solve the following equation by...

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  14. 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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  15. Prove the following: [[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2...

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  16. 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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  17. If D=abs((a,b,c),(c,a,b),(b,c,a)) and D'=abs((b+c,c+a,a+b),(a+b,b+c,c+...

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  18. Show that abs((2(a+b+c),a,b),(2(a+b+c),b+c+2a,b),(2(a+b+c),a,c+a+2b))=...

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  19. 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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  20. Prove that the following. [[b^2+c^2,ab,ac],[ab,c^2+a^2,bc],[ca,cb,a^2+...

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