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Prove that: {:|(1,x,x^3),(1,y,y^3),(1,...

Prove that:
`{:|(1,x,x^3),(1,y,y^3),(1,z,z^3)| = (x-y)(y-z)(z-x)(x+y+z)`

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Prove that |(1,x,x^2),(1,y,y^2),(1,z,z^2)| = (x-y)(y-z)(z-x)

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Prove that: {:|(x,y,z),(x^2,y^2,z^2),(x^3,y^3,z^3)|=|(x,x^2,x^3),(y,y^2,y^3),(z,z^2,z^3)| = xyz(x-y(y-z)(z-x)

Prove the following identities : |{:(x,x^(2),x^(3)),(y,y^(2),y^(3)),(z,z^(2),z^(3)):}|=xyz(x-y)(y-z)(z-x) .

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Using properties of determinants, prove that: |[x,x^2,1+px^3],[y,y^2,1+py^3],[z,z^2,1+pz^3]| = (1+pxyz)(x-y)(y-z)(z-x)

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PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. Prove that: {:|(1,x,x^3),(1,y,y^3),(1,z,z^3)| = (x-y)(y-z)(z-x)(x+y+...

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  2. If A = [(13,-10),(7,87)], write the following submatrices of A. A12

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  3. If A = [(13,-10),(7,87)], write the following submatrices of A. A22

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  4. If A = [(a,h,g),(h,b,f),(g,f,c)], find the submatrix of A obtained by ...

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  5. If A = [(a,h,g),(h,b,f),(g,f,c)], find the submatrix of A obtained by ...

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  6. If A = [(a,h,g),(h,b,f),(g,f,c)], find the submatrix of A obtained by ...

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  7. If A = [(a,h,g),(h,b,f),(g,f,c)], find the submatrix of A obtained by ...

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  8. Find the minors and cofactos of each entry of the first column of the ...

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  9. Find the minors and cofactos of each entry of the first column of the ...

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  10. Find the minors and cofactos of each entry of the first column of the ...

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  11. Find the minors and cofactos of each entry of the first column of the ...

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  12. Evaluate the following determinants: {:|(-2,3),(4,-9)|

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  13. Evalate the following determinants: |(1//2, 8),(4,2)|

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  14. Evaluate the following determinants: |(a+ib , - c + id),(c+id, a-ib)...

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  15. Evaluate the following determinants: |(3x, x-7),(x+1,5x+1)|

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  16. Show that |(sin10^@, - cos10^@),(sin80^@, cos80^@)| = 1

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  17. Show that {:|(cos15^@, sin15^@),(sin75^@, cos75^@)|:}= 0

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  18. Evaluate |(x,x+1),(x-1,x)|

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  19. Evaluate the following determinants: |(1,0,0),(0,1,0),(0,0,1)|

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  20. Evaluate the following determinants: |(1,-3,3),(4,-1,3),(3,5,3)|

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  21. Evaluate the following determinants: |(1,0,2),(0,2,1),(2,0,3)|

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