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Consider the determinant Delta =|[1,a,a...

Consider the determinant
`Delta =|[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-ba]|`Without expanding, prove that `Delta=0`

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A N EXCEL PUBLICATION-DETERMINANTS-QUESTION TYPE
  1. Consider the determinant D=|[1,3,5],[2,6,10],[31,11,38]| Evaluate De...

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

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

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

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

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

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

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

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

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

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

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

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

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  14. Using properties of determinants prove the following. abs[[1,1,1],...

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

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  16. By using properties of determinants, prove that |[x+4,2x,2x],[2x,x+4,...

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  17. By using properties of determinants, prove that |[y+k,y,y],[y,y+k,y],...

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  18. Prove that abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

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

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

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