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|(1/a,a^2,bc),(1/b,b^2,ca),(1/c,c^2,ab)|...

`|(1/a,a^2,bc),(1/b,b^2,ca),(1/c,c^2,ab)|=`

A

abc

B

`1/(abc)`

C

`ab+bc+ca`

D

0

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The correct Answer is:
D
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Without expanding the determinant , prove that |{:(a, a^(2),bc),(b,b^(2),ca),(c,c^(2),ab):}|=|{:(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3)):}|

Prove the following : |{:(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab):}|=|{:(a,a^(2),bc),(b,b^(2),ca),(c,c^(2),ab):}|=(ab+bc+ca)(a-b)(b-c)(c-a) .

Show without expanding at any stage that: [1/a, a^2, bc],[1/b, b^2, ca],[1/c, c^2, ab]|=0

|[1,a^(2),bc],[1,b^(2),ca],[1,c^(2),ab]|

|[a,a^(2),bc],[b,b^(2),ca],[c,c^(2),ab]|=|[1,a^(2),a^(3)],[1,b^(2),b^(3)],[1,c^(2),c^(3)]|

The determinants |{:(1,a, bc),(1, b, ca),(1, c, ab):}| " and "|{:(1,a, a^(2)),(1, b, b^(2)),(1, c, c^(2)):}| are not identically equal.

The value of |(a,a^(2) - bc,1),(b,b^(2) - ca,1),(c,c^(2) - ab,1)| , is

Show without expanding at any stage that: [a,a^2,bc],[b,b^2,ca],[c,c^2,ab]|=|[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|

ML KHANNA-DETERMINANTS -Self Assessment Test
  1. If a != b != c, are value of x which satisfies the equation |(0,x -a...

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  2. |(b+c,a,a),(b,c+a,b),(c,c,a+b)|=

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

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

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  5. If x=-9 is a root of |(x,3,7),(2,x,2),(7,6,x)|=0 then other two roots ...

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  6. The solution of the equation |(x,2,-1),(2,5,x),(-1,2,x)| = 0 are

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  7. The roots of the equation |(0,x,16),(x,5,7),(0,9,x)| = 0 are

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  8. |(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)|=k|(a,b,c),(b,c,a),(c,a,b)|...

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  9. A root of the equation |(3-x,-6,3),(-6,3-x,3),(3,3,-6-x)| = 0

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  10. If |(-a^2,ab,ac),(ab,-b^2,bc),(ac,bc,-c^2)|=ka^2b^2c^2 , then k =

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  11. If omega!=1 is a cube root of unity and Delta=|(x+omega^(2),omega,1)...

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  12. |((a^x+a^(-x))^2,(a^x-a^(-x))^(2),1),((b^x+b^(-x))^2,(b^x-b^(-x))^(2),...

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  13. The number of values of k which the linear equations 4x+ky+2z=0 kx...

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  14. The value of k for which the set of equationsx + ky + 3z=0, 3x + ky – ...

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  15. If x + y +z=0, 4x+3y -z=0 and 3x + 5y +3z=0 is the given system of equ...

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  16. The system of equations x + y + z=2, 3x – y +2z=6 and 3x + y +z=-18 ha...

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  17. The system of equations x+y+z=6, x+2y + 3z= 10, x+2y + lamdaz=mu has n...

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  18. The system of linear equations x1 + 2x2 + x3 = 3, 2x1 + 3x2 + x3 = 3...

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  19. Let a,b,c be such that b(a+c) ne 0 . If |(a,a+1,a-1),(-b,b+1,b-1),(c...

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