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Show that |^x Cr^x C(r+1)^x C(r+2)^y Cr^...

Show that `|^x C_r^x C_(r+1)^x C_(r+2)^y C_r^y C_(r+1)^y C_(r+2)^z C_r^z C_(r+1)^z C_(r+1)|=|^x C_r^(x+1)C_(r+1)^(x+2)C_(r+2)^y C_r^(y+1)C_(r+1)^(y+2)C_(r+2)^z C_r^(z+1)C_(r+1)^(z+2)C_(r+1)|` .

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CENGAGE-DETERMINANTS-All Questions
  1. The determinant |x p+y x y y p+z y z0x p+y y p+z|=0 if x ,y ,z

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  2. Using properties of determinant prove that |a+b+c-c-b-c a+b+c-a-b-a a...

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  3. Show that |^x Cr^x C(r+1)^x C(r+2)^y Cr^y C(r+1)^y C(r+2)^z Cr^z C(r+1...

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  4. If omega!=1 is a cube root of unity and x+y+z!=0, then prove tha...

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  5. Statement 1: If the system of equation lambdax+(b-a)y+(c-a)z=0,(a-b)x+...

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  6. If A , Ba n dC are the angels of a triangle, show that |-1+cos B co...

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  7. If alpha,beta,gamma are the angles of a triangle and system of equatio...

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  8. Without expanding the determinants, prove that |103 115 114 111 108 10...

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  9. Given a=x//(y-z), b=y//(z-x),a n dc=z//(x-y),w h e r ex , y , za n dz ...

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  10. Find the value of determinant |(sqrt((13))+sqrt(3),2sqrt(5),sqrt(5))sq...

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  11. a ,b ,c are distinct real numbers not equal to one. If a x+y+z=0,x+b y...

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  12. Prove that the value of the determinant |-7 5+3i2/3-4i5-3i8 4+5i2/3+4i...

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  13. If the system of linear equation x+y+z=6,x+2y+3c=14 ,a n d2x+5y+lambda...

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  14. If ar=(cos2rpi+is in2rpi)^(1//9) , then prove that |a1a2a3a4a5a6a7a8a9...

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  15. Let f(x)=|2cos^2xsin2x-sinxsin2x2sin^2xcosxsinx-cosx0| . Then the val...

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  16. Using properties of determinants, prove that |(-a^2,ab,ac),(ba,-b^2,bc...

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  17. The number of positive integral solutions of the equation |(x^3+1,x^2y...

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  18. If the value of determinant |(a,1,1),(1,b,1)(1,1,c)| is positive , the...

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  19. By using properties of determinants. Show that: (i) |(x+4,2x,2x),(2x,x...

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  20. Using properties of determinants, evaluate |18 40 89 40 89 198 89 198 ...

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