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Without expanding the determinant prove ...

Without expanding the determinant prove that
`abs([a,a^2,bc],[b,b^2,ca],[c,c^2,ab])=abs([1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3])`

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|[a,a^(2),bc],[b,b^(2),ca],[c,c^(2),ab]|=|[1,a^(2),a^(3)],[1,b^(2),b^(3)],[1,c^(2),c^(3)]|

Show without expanding at any stage that: [a,a^2,bc],[b,b^2,ca],[c,c^2,ab]|=|[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|

Without expanding the determinant , prove that |{:(a, a^(2),bc),(b,b^(2),ca),(c,c^(2),ab):}|=|{:(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3)):}|

Without expanding the determinant,prove ,a,a^(2),bcb,b^(2),cac,c^(2),ab]|=det[[1,a^(2),a^(3)1,b^(2),b^(3)1,c^(2),c^(3)]]

Show without expanding at any stage that: [1/a, a^2, bc],[1/b, b^2, ca],[1/c, c^2, ab]|=0

Without expanding prove that: |[1,a,a^(2)-bc],[1,b,b^(2)-ca],[1,c,c^(2)-ab]|=0

Prove that |[1,a,bc] , [1,b,ca], [1,c,ab]|=|[1,a,a^2] , [1,b,b^2] , [1,c,c^2]|

Show without expanding at any stage that: [1/a, a,bc],[1/b,b,ca],[1/c, c, ab]|=0

Prove that det[[1,a,a^(2)-bc1,b,b^(2)-ca1,c,c^(2)-ab]]=0

MAHAVEER PUBLICATION-DETERMINANTS-QUESTION BANK
  1. Show that abs([x,b,c],[x,b,y],[y,b,c])=b(x-y)(c-y)

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  2. Prove that the determinate abs([x,sintheta,costheta],[-sintheta,-x,1],...

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  3. Without expanding the determinant prove that abs([a,a^2,bc],[b,b^2,...

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  4. Solve the equation |x+a xxxx+a xxxx+a|=0, a!= 0

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  5. Find minors and cofactors of all the elements of the determinant abs([...

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  6. Solve by Cramer's rule: 3x-2y=4 6x-y=11

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  7. Solve by Cramer's rule: 3x+2y=4 8x+3y=13

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  8. Solve by Cramer's rule: 3x-2y=4 x-4y=-2

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  9. Solve by cramer's rule : 3x-5y=21 5x+y=7

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  10. Solve by cramer's rule : x+y+z=3 2x-y+3z=4 x+2y-z=2

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  11. Evaluate the determinates abs([2,3],[1,7])

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  12. Evaluate the determinates abs([-costheta,-sin theta],[sintheta,-costhe...

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  13. Evaluate the determinatesabs([3,-4,5],[1,1,-2],[2,3,1])

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  14. Evaluate the determinates abs([2,-1,-2],[0,2,-1],[3,-5,0])

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  15. Find the value of x is abs([3,x],[x,1])=abs([3,2],[4,1])

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  16. Find the value of x is abs([2,3],[4,5])=abs([x,3],[2x,5])

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  17. Using the property of determinants and without expanding prove that ab...

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  18. Using the property of determinants and without expanding, prove that:...

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  19. Using the property of determinants and without expanding, prove that:...

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  20. Using the property of determinants and without expanding prove that ab...

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