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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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A N EXCEL PUBLICATION-DETERMINANTS-QUESTION TYPE
  1. prove that abs[[a,b,c],[a+2x,b+2y,c+2z],[x,y,z]]=0

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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, prove that |[1,omega,omega^2],[omega,omega^2,1],[om...

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

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

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  7. Consider the determinant D=|[1,3,5],[2,6,10],[31,11,38]| On taking 2 ...

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  8. Consider the determinant D=|[1,3,5],[2,6,10],[31,11,38]| Evaluate De...

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  9. Consider the determinant Delta =|[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-b...

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  10. Consider the determinant Delta =|[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-b...

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  11. Consider the equation |[3x-8,3,3],[3,3x-8,3],[3,3,3x-8]|=0 OperatingC1...

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  12. Consider the equation |[3x-8,3,3],[3,3x-8,3],[3,3,3x-8]|=0 Solve the ...

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

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  14. Without expanding the determinant prove the following. |[2,7,65],[3,...

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

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  16. Without expanding the determinant prove the following. |[1,bc,a(b+c)...

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

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

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

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  20. using properties of determinants, prove that abs[[1,a,a^2],[1,b,b^2],...

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