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

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

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

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)):}|

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

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

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

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

|{:(1,a,bc),(1,b,ca),(1,c,ab):}|=|{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|

Prove |{:(1,a^2+bc,a^3),(1,b^2+ca,b^3),(1,c^2+ab,c^3):}|=-(a-b)(b-c)(c-a)(a^2+b^2+c^2)

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

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

CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B
  1. If A,B,C , are the angles of a triangles, show that, |{:(sin^2A,coaA,1...

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  2. without expanding prove that [22-24] |{:(7,12,-3),(9,14,-1),(8,13,-2...

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  3. |{:(1,bc,bc(b+c)),(1,ca,ca(c+a)),(1,ab,ab(a+b)):}|=0

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  4. |{:(logx xyz,logxy,logxz),(logyxyz,1,logyz),(logzxyz,logzy,1):}|=0

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  5. if |{:(a+ib,c+id),(-c+id,a-ib):}|xx|{:(alpha-ibeta,gamma-idelta),(-gam...

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  6. |{:(-a(b^2+c^2-a^2)," "2b^3," "2c^3),(" ...

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  7. Show that |{:(x-3,x-4,x-alpha),(x-2,x-3,x-beta),(x-1,x-2,x-gamma):}|=0...

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  8. If a, b, c, are real numbers such that |{:(b+c,c+a,a+b),(c+a,a+b,b+c...

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  9. Show that , |{:((a^2+b^2)/c," "c," "c),(" "a,(b^2+c^2)/a," "a),(" "b,"...

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  10. prove that , |{:(1,1+a,1+a+b),(2,3+2a,4+3a+2b),(3,6+3a,10+6a+3b):}|=1

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  11. if f(x) =|{:(sinx,cosx,tanx),(x^3,x^2,x),(2x,1,1):}| then show that li...

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  12. If 5 is one root of the equation |{:(x,3,7),(2,x,-2),(7,8,x):}|=0 then...

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  13. If y =sinpx and yn is the nth derivative of y , then find the value...

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  14. If |{:(1+ax,1+bx,1+cx),(1+a1x,1+b1x,1+c1x),(1+a2x,1+b2x,1+c2x):}|=A0+A...

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  15. Evaluate: |{:(1,1,1),(1,omega^2,omega),(1,omega,omega^2):}| (where ome...

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  16. If |{:(-a^2," "ab," "ac),(" "ab,-b^2," "bc),(" "ac," "bc,-c^2):}|=lamb...

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  17. If |{:(10(c(4)),10(c(5)),11(c(m))),(11(c(6)),11(c(7)),12(c(m+2))),(12(...

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  18. If l,m and n are real numbers such that l^2+m^2+n^2=0 , then show t...

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  19. If f(x)= |{:(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),x(x+1)(x...

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  20. If omega ne 1 is a cube root of unity , then find the value of |{:(...

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