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Evaluate the following determinates |{...

Evaluate the following determinates
`|{:(1,omega),(omega,-omega):}|` where `omega` is the cube root of unity

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Using the property of determinants and without expanding prove the following |{:(1,omega^n,omega^(2n)),(omega^(2n),1,omega^n),(omega^n,omega^(2n),1):}|=0 where omega is a cube root of unity

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If x, y, z are not all zero & if ax + by + cz=0, bx+ cy + az=0 & cx + ay + bz = 0 , then prove that x: y : z = 1 : 1 : 1 OR 1 :omega:omega^2 OR 1:omega^2:omega , where omega is one ofthe complex cube root of unity.

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KUMAR PRAKASHAN-DETERMINANTS -Practice Work
  1. Evaluate the following determinates |{:(x,y),(-y,x):}|

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  2. Evaluate the following determinates |{:(1,omega),(omega,-omega):}| w...

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  3. Evaluate the following determinates |{:(sin10^@,-cos10^@),(sin80^@, ...

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  4. Evaluate the following determinates |{:(1+2hati,1-hati),(1+hati,1-2h...

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  5. Evaluate the following determinates |{:(logab,1),(1,logba):}|

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  6. Evaluate the following determinates |{:(-1,3,4),(1,9,12),(9,9,12):}|

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  7. Evaluate the following determinates |{:(0,1,sectheta),(tantheta,-sec...

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  8. If |{:(x+1,x-1),(x-3,x+2):}|=|{:(4,-1),(1,3):}| then find x

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  9. If |{:(1,2,x),(1,1,1),(2,1,-1):}|=0 then find x.

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  10. If |{:(4,x),(-3,5):}|=8 then find x.

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  11. If |{:(m,-2),(5,2m):}|=|{:(5,-4),(5,3):}| then find m

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  12. If |{:(x,1,2),(1,0,3),(5,-1,4):}|=0 then find x

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  13. Using the property of determinants and without expanding prove the fol...

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  14. Using the property of determinants and without expanding prove the fol...

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  15. Using the property of determinants and without expanding prove the fol...

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  16. Using the property of determinants and without expanding prove the fol...

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  17. Using the property of determinants and without expanding prove the fol...

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  18. Using the properties of determinants, solve the following for x |{:(...

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  19. Prove that |{:(a+1,1,1),(1,b+1,1),(1,1,c+1):}|=abc(1/a+1/b+1/c+1)

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  20. Using the properties of determinants, prove the following |{:((b+c)^...

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