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Using properties of determinants, show...

Using properties of determinants,
show that
`abs[[a,a^2,b+c],[b,b^2,c+a],[c,c^2,a+b]]=(b-c)(c-a)(a-b)(a+b+c)`

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BODY BOOKS PUBLICATION-DETERMINANTS-EXERCISE
  1. Show that abs[[a+b,b+c,c+a],[b+c,c+a,a+b],[c+a,a+b,b+c]]=2abs[[a,b,c],...

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  2. The value of the determinant |(sin10,-cos10),(sin50,cos50)| is a)-1 b)...

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  3. Using properties of determinants, show that abs[[a,a^2,b+c],[b,b^2...

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  4. Choose the correct answer from the bracket.The value of the determin...

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  5. Consider abs[[a,a+b,a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b,10a+6b+3c]]

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  6. Choose the correct answer from the bracket.Consider a sqare matrix o...

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  7. Verify A(adjA)=(adjA)A=abs[A]I for the matrix A=[[5,-2],[3,-2]]that,...

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  8. Choose the correct answer from the bracket. If A=[(cosx,sinx),(-sinx,c...

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  9. Find the inverse of the following A=[[1,-1,2],[0,2,-3],[3,-2,4]]

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  10. If A=[[2,3],[1,-2]] and A^-1=kA,then the value of 'k' is

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  11. If A=[[1,-1,1],[2,-1,0],[1,0,0]], Find A^2

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  12. If A=[[1,-1,1],[2,-1,0],[1,0,0]], Show that A^2=A^-1

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  13. Choose the correct answer. If each element of a third order square mat...

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  14. Consider the matrix A=[(-8,5),(2,4)] Show that 'A' satisfies the equat...

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  15. Consider the matrix A=[(-8,5),(2,4)] Hence find A^-1.

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  16. If A and B are matrices of order 3 such that abs[A]=-1,abs[B]=3,then...

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  17. If A=[(1,tanx),(-tanx,1)], Show that, A^TA^-1=[(cos2x,-sin2x),(sin2x,c...

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  18. If A=[[1,1,5],[0,1,3],[0,-1,-2]] what is the value of abs[3A]?

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  19. Find the equation of the line joining the points(1,2) and (-3,-2) us...

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  20. Find the values of x in which abs[[3,x],[x,1]]=abs[[3,2],[4,1]]

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