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|{:(1,a,bc),(1,b,ca),(1,c,ab):}|...

`|{:(1,a,bc),(1,b,ca),(1,c,ab):}|`

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The correct Answer is:
(b-c)(c-a)(a-b)
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|{:(1,1,1),(a,b,c),(bc,ca,ab):}|=(a-b)(b-c)(c-a)

Without expanding prove that, |{:(1,bc,b+c),(1,ca,c+a),(1,ab,a+b):}|=|{:(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2)):}|

|{:(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):}|

If |{:(a,b,1),(b,c,1),(c,a,1):}|=2010 and if |{:(c-a,c-b,ab),(a-b,a-c,bc),(b-c,b-a,ca):}|-|{:(c-a,c-b,c^(2)),(a-b,a-c,a^(2)),(b-c,b-a,b^(2)):}|=p , then the number of positive divisors of p is

|{:(1,bc,a(b+c)),(1,ca,b(c+a)),(1,ab,c(a+b)):}|=0

Evalute |{:(0,c,b),(c,0,a),(b,a,0):}| and hence show that, |{:(" "-a^2," "ab," "ac),(" "ab," "-b^2," "bc),(" "ca," "bc," "-c^2):}|=4a^2b^2c^2

|{:(1,bc,bc(b+c)),(1,ca,ca(c+a)),(1,ab,ab(a+b)):}|=0

If D=|(1,a,a^(2)-bc),(1,b,b^(2)-ca),(1,c,c^(2)-ab)| , then D is -

Without expanding prove that , |{:(1,ab,1/a+1/b),(1,bc,1/b+1/c),(1,ca,1/c+1/a):}|=0

Without expanding prove that |{:(1,a,a^(2)-bc),(1,b,b^(2)-ca),(1,c,c^(2)-ab):}|=0

CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2A
  1. |{:(" "1," "4,-3),(-4," "1," "2),(" "3,-2," "1):}|

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  2. |{:(x,z,0),(0,y,y),(z,0,x):}|

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  3. |{:(1,a,bc),(1,b,ca),(1,c,ab):}|

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  4. |{:(1," "1," "1),(1,1+x," "1),(1," "1,1+y):}|

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  5. |{:(1+a," "b," "c),(" "a,1+b," "c),(" "a," "b,1+c):}|

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  6. |{:(" "1," "z,-y),(-z," "1," "x),(" "y,-x," "1):}|

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  7. |{:(-a," "a," "a),(" "b,-b," "b),(" "c," "c,-c):}|

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  8. |{:(0," "sinalpha,-cosbeta),(cosalpha," "0," "sinbeta),(cos alpha,-sin...

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  9. write minor and cofactor ; |{:(5,2),(0,-1):}|

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  10. write minor and cofactor ; |{:(-1,4),(2,3):}|

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  11. write down the minor and cofactor |{:(1,a,bc),(1,b,ca),(1,c,ab):}|

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  12. write down the minor and cofactor |{:(0,2,6),(1,5,0),(3,7,1):}|

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  13. Evaluate the determinant |{:(" "2,3,-5),(" "7,1,-2),(-3,4," "1):}| ...

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  14. If [.] denotes the greatest ingeter less then or equal to the real num...

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  15. Evalute the determinant D=|{:(" "1," "sintheta,1),(-sintheta," "1,si...

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  16. Find the minors and the cofactors of each element of the first column ...

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  17. If A=[{:(1,3),(2,1):}],find the determinant of the matrix A^2-2A.

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  18. If A =[{:(1,0,1),(0,1,2),(0,0,4):}], then show that |3A|=27|A|.

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  19. If A = [{:(2,5),(2,1):}] and B =[{:(4,-3),(2,5):}] ,verify that |AB|...

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  20. If f(theta)=|{:(cos^2theta,costhetasintheta,-sintheta),(costhetasinthe...

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