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If omega is a cube root of unit, then De...

If `omega` is a cube root of unit, then `Delta=|(x+1,omega, omega^(2)),(omega, x+omega^(2),1),(omega^(2),1,x+omega)|=`

A

`x^(3)+1`

B

`x^(3)+omega`

C

`x^(3)+omega^(2)`

D

`x^(3)`

Text Solution

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The correct Answer is:
D
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DIPTI PUBLICATION ( AP EAMET)-MATRICES-EXERCISE 1B MCQ (DETERMINANTS)
  1. If A=|(b^(2)c^(2),bc,b+c),(c^(2)a^(2),ca,c+a),(a^(2)b^(2),ab,a+b)| the...

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  2. The determinant Delta=|(a,a+b,a+2b),(a+2b,a,a+b),(a+b,a+2b,a)|=

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  3. If omega is a cube root of unit, then Delta=|(x+1,omega, omega^(2)),(o...

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  4. |(1,1,1),(a,b,c),(a^(2)-bc,b^(2)-ca,c^(2)-ab)|=

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  5. |(x,x^(2),1+x^(3)),(y,y^(2),1+y^(3)),(z,z^(2),1+z^(2))|=0,x!=y!=zimpli...

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  6. If |(a,a^(2),1+a^(3)),(b,b^(2),1+b^(3)),(c,c^(2),1+c^(3))|=0 and vecto...

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  7. If a,b,c are all different and |(a,a^(3),a^(4)-1),(b,b^(3),b^(4)-1),(c...

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  8. If a,b,c are different and |(a,a^(2),a^(3)-1),(b,b^(2),b^(3)-1),(c,c^(...

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  9. If a,b,c are all different and |(1+a^(2),1+b^(2),1+c^(2)),(a,b,c),(a^(...

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  10. If p+q+r=0 and |(pa,qb,rc),(qc,ra,pb),(rb,pc,qa)|=k|(a,b,c),(c,a,b),(b...

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  11. If Delta=|(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))|=k(a-b)(b-c)(c-a) then k...

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  12. If abc!=0 and if |(a,b,c),(b,c,a),(c,a,b)|=0 then (a^(3)+b^(3)+c^(3))/...

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  13. |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))|=

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  14. Let A=[(5,5 alpha, alpha),(0, alpha, 5 alpha),(0,0,5)] If |A|^(2)=25 t...

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  15. If k gt1, and the determinant of the matrix A^(2), where A=[(k,kalpha,...

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  16. If a!=6,b,c satisfy |(a,2b,2c),(3,b,c),(4,a,b)|=0 then abc

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  17. If a!=6,b,c satisfy |(a,2b,2c),(3,b,c),(4,a,b)|=0 then abc

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  18. If f(x)=|(a,-1,0),(ax,a,-1),(ax^(2),ax,a)| then f(3x)-f(2x)=

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  19. If Delta=|(a,1,1),(1,b,1),(1,1,c)|gt0, then

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  20. If A is a 3xx3 matrix and det(3A)=k(detA) then k=

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