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Consider the determinant Delta=abs[[x,x^...

Consider the determinant `Delta=abs[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,1+z^3]]`,
Where x,y,z are different.
Show that if `Delta=0`,then`1+xyz=0`

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Consider the determinant Delta=abs[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,1+z^3]] , Where x,y,z are different. Express the above determinant as sum of two determinants.

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Prove that abs[[1,x,x^2],[1,y,y^2],[1,z,z^2]]=(x-y)(y-z)(z-x)

Given Delta=|(x,x^2,1+px^3),(y,y^2,1+py^3),(z,z^2,1+pz^3)| Prove that Delta=(1+pxyz)(x-y)(y-z)(z-x) .

Without expanding prove that abs[[x+y,y+z,z+x],[z,x,y],[1,1,1]]=0

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V PUBLICATION-DETERMINANT-QUESTION BANK
  1. Evaluate Delta=|[1, a, bc],[ 1, b, c a],[ 1, c, a b]|

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  2. Using properties of determinants prove the following. abs[[b+c,a,...

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  3. Consider the determinant Delta=abs[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,...

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

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  5. Without expanding the determinant prove the following. |[x,a,x+a],[y...

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  6. Without expanding the determinant prove the following. |[a-b,b-c,c-a...

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  7. Evaluate |[2, 7, 65],[ 3, 8, 75],[ 5, 9, 86]|=0

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  8. prove |[1, b c, a(b+c)],[ 1, c a, b(c+a)],[ 1, a b, c(a+b)]|=0

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  9. Without expanding the determinant prove the following. |[b+c,q+r,y+z...

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  10. By using properties of determinants, prove that |[0,a ,-b],[-a,0,-c],...

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  11. By using properties of determinants, prove that |[-a^2,ab,ac],[ba,-b^...

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  12. Show that abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a)

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  13. By using properties of determinants, prove that |[x,x^2,yz],[y,y^2,zx...

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  14. Prove that abs[[y+k,y,y],[y,y+k,y],[y,y,y+k]]=k^2(3y+k)

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  15. By using properties of determinants, prove that |[x+y+2z,x,y],[z,y+z+...

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  16. Using properties of determinants prove the following. abs[[1,x,x^2...

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  17. Prove |[1+a^2-b^2, 2 a b, -2 b],[ 2 a b, 1-a^2+b^2, 2 a],[ 2 b,...

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  18. By using the properties of determinants,prove that |[a^2+1,ab ,ac],[a...

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  19. Let A be a square matrix of order 2x2 thenabs[KA] is equal to

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  20. Which of the following is correct? a)Determinant is a square matrix ...

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