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Using properties of determinants show ...

Using properties of determinants show
that
`abs[[1+a,1,1],[1,1+b,1],[1,1,1+c]]=abc(1+1/a+1/b+1/c)`

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using properties of determinants, prove that abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a) .

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The value of the determinant abs[[1,1,1],[1,-1,-1],[1,1,-1]] is

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MAXIMUM PUBLICATION-DETERMINANTS-EXAMPLE
  1. Consider abs[[a,a+b,a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b,10a+6b+3c]]

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  2. Letabs[[1,3,2],[2,0,1],[3,4,3]]=3,then what is the value ofabs[[1,3,...

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  3. Using properties of determinants show that abs[[1+a,1,1],[1,1+b,1]...

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  4. IfA=[[2,-3,5],[3,2,-4],[1,1,-2]] Findabs[A]

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  5. IfA=[[2,-3,5],[3,2,-4],[1,1,-2]] Find adjA.

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  6. LetA=[[1,-1,1],[2,1,-3],[1,1,1]] is A singular?

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  7. LetA=[[1,-1,1],[2,1,-3],[1,1,1]] Find adjA.

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  8. Let A=[[1,-1,1] ,[2,1,-3] ,[1,1,1]] Obtain A^-1.

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  9. LetA=[[1,-1,1],[2,1,-3],[1,1,1]] Using A^-1 solve the system of eq...

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  10. Solve the following system of linear equations. x+y+z=3, y-z=0, ...

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  11. Solve the following system of linear equations. x+2y+5z=10, x-y-...

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  12. If f(x)=[[cosx,-sinx,0],[sinx,cosx,0],[0,0,1]] Find f(-x)

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  13. Solve the following system of linear equations. x+2y+5z=10, x-y-...

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  14. Solve the following system of linear equations. x+y+z=3, y-z=0, ...

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

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

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

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  18. Arjun' purchased 3 pens,2 purses and 1 instrument box and pays Rs. 410...

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  19. Arjun' purchased 3 pens,2 purses and 1 instrument box and pays Rs. 4...

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  20. If A=[[2,-3,5],[3,2,-4],[1,1,-2]] Find A^-1

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