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Show that abs([y+z ,x,x],[y,z+x,y],[z,z,...

Show that `abs([y+z ,x,x],[y,z+x,y],[z,z,x+y])=4xyz`

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|[z+y,x,x] , [y,z+x,y] , [z,z,x+y]|=

Using the properties of determinants, show that: abs((x,x^2,yz),(y,y^2,xz),(z,z^2,xy))=(x−y)(y−z)(z−x)(xy+yz+zx)

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prove that: |(y+z,z,y),(z,z+x,x),(y,x,x+y)|=4xyz

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show that [[y+x,x+x,x+yz+x,x+y,y+zx+y,y+z,z+x]]=-2(x^(3)+y^(3)+z^(3)-3xyz)

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Prove that |[x+y, y+z, z+x] , [z+x, x+y, y+z] , [y+z, z+x, x+y]|=2|[x,y,z] , [z,x,y] , [y,z,x]|

MAHAVEER PUBLICATION-DETERMINANTS-QUESTION BANK
  1. (iii) सारणिक का बिना विस्तार किये हुए सिद्ध करें कि |{:(a,b,c),(x,y,z)...

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  2. Prove that : Det[[x,x^2,x^3],[y,y^2,y^3],[z,z^2,z^3]]=xyz(x-y)(y-z)(z-...

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  3. Show that abs([y+z ,x,x],[y,z+x,y],[z,z,x+y])=4xyz

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  4. Show that abs([x,b,c],[x,b,y],[y,b,c])=b(x-y)(c-y)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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