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Show that : The value of Delta=abs([1,0,...

Show that : The value of `Delta=abs([1,0,3],[0,1,0],[1,0,2])=-1`

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MAHAVEER PUBLICATION-DETERMINANTS-QUESTION BANK
  1. Find the value of x if abs([x,2],[18,x])=abs([6,2],[18,6])

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  2. Find the value of abs(2A) if A= abs([1,0,1],[0,1,0],[1,0,2])

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  3. Show that : The value of Delta=abs([1,0,3],[0,1,0],[1,0,2])=-1

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  4. Delta=abs([1xx5,2xx5,3xx5],[3,1,6],[4,2,1])=5abs([1,2,3],[3,1,6],[4,2,...

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  5. Evaluate abs([2,4,0],[-1,1,2],[0,-2,1])

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  6. Evalaute abs([2,3,4],[8,12,6],[97,98,99])

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  7. Evaluate abs([23,13,4],[42,39,12],[67,52,16])

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  8. Evaluate abs([98,81,321],[88,72,423],[55,45,657])

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  9. Evaluate abs([a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c])

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  10. Prove that abs([1,1,1],[1,1+a,1],[1,1,1+b])=ab

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  11. ([1,1,1],[a,b,c],[a^2,b^2,c^2])=(a-b)(b-c)(c-a)

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  12. (iii) सारणिक का बिना विस्तार किये हुए सिद्ध करें कि |{:(a,b,c),(x,y,z)...

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

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

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

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

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

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

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

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