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|{:(logx xyz,logxy,logxz),(logyxyz,1,log...

`|{:(log_x xyz,log_xy,log_xz),(log_yxyz,1,log_yz),(log_zxyz,log_zy,1):}|=0`

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prove that, |{:(" "1,log_xy,log_xz),(log_yx," "1,log_yz),(log_zx,log_zy," "1):}|=0

Prove that |[1,log_xy,log_xz],[log_yx,1,log_yz],[log_zx,log_zy,1]|=0

If x, y and z be greater than 1, then the value of |(1,log_(x)y,log_(x)z),(log_(y)x,1,log_(y)z),(log_(z)x,log_(z)y,1)| is

Prove that , |[1,log_x^y,log_x^z],[log_y^x,1,log_y^z],[log_z^x,log_z^y,1]|=0

Show that |[1,log_ab,log_ac],[log_ba,1,log_bc],[log_ca,log_cb,1]|=0 ,(a>0,b>0,c>0)

Prove that the value of each the following determinants is zero: |[logx,logy,logz],[ log2x ,log2y ,log2z ],[log3x, log3y ,log3z]|

The value of |(log_(3)512,log_(4)3),(log_(3)8,log_(4)9)|xx|(log_(2)3,log_(8)3),(log_(3)4,log_(3)4)| is -

Solve : log_(2)log_(2)log_(2)x=-1

Find the value of (yz)^(log y - log z) xx (zx)^(log z - log x) xx (xy)^(log x - log y) .

If a,b,c be three such positive numbers (none of them is 1) that (log_(b)a log_(c )a-log_(a)a) + (log_(a)b log_(c )b-log_(b)b) + (log_(a)c log_(b)c-log_(c )c) = 0 , the prove that abc = 1.

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

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  2. |{:(1,bc,bc(b+c)),(1,ca,ca(c+a)),(1,ab,ab(a+b)):}|=0

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

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

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

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  6. 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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  7. 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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  8. Show that , |{:((a^2+b^2)/c," "c," "c),(" "a,(b^2+c^2)/a," "a),(" "b,"...

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

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

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

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

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

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

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

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

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