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Prove that: |[x,x^2,yz],[y,y^2,zx],[z,z^...

Prove that: `|[x,x^2,yz],[y,y^2,zx],[z,z^2,xy]|=(x-y)(y-z)(z-x)(xy+yz+zx)`

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Prove that |[1,x,x^2-yz],[1,y,y^2-zx],[1,z,z^2-xy]|= 0

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

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

Using the properties of determinants, show that : |[[x^2, y^2, z^2],[yz, zx, xy],[x,y,z]]|= (x-y)(y-z)(z-x)(xy+yz+zx) .

Prove that |[[x,y,z],[x^2,y^2,z^2],[x^3,y^3,z^3]]|= xyz (x-y)(y-z)(z-x)

Show that |(1,x^2,x^3),(1,y^2,y^3),(1,z^2,z^3)| = (x-y),(y-z)(z-x)(xy+yz+zx)

Using the properties of determinant, show that : |[1,x+y,x^2+y^2],[1,y+z,y^2+z^2],[1,z+x,z^2+x^2]| = (x-y)(y-z)(z-x)

Prove that : |[x+y+z,-z,-y],[-z, x+y+z, -x],[-y,-x,x+y+z]|= 2(x+y)(y+z)(z+x)

PSEB-DETERMINANTS-Exercise
  1. By using properties of determinants, show that : |[1,1,1],[a,b,c],[a^...

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  2. By using properties of determinants, show that : |[x+4,2x,2x],[2x,x+4...

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  3. Prove that: |[x,x^2,yz],[y,y^2,zx],[z,z^2,xy]|=(x-y)(y-z)(z-x)(xy+yz+z...

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  4. Prove that : |[y+k,y,y],[y,y+k,y],[y,y,y+k]|=k^2(3y+k).

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  5. Show that: |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3

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  6. By using properties of determinants, show that : |[x+y+2z,x,y],[z,y+...

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  7. By using properties of determinants, show that : |[1,x,x^2],[x^2,1,x...

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  8. Using the properties of determinant, show that :|[a^2+1,ab,ac],[ab,b^2...

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  9. Let A be a square matrix of order 3 xx 3. Then I kA I is equal to :

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  10. Which of the following is correct

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  11. Find area of the triangle with vertices at the point given in the fol...

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  12. Find area of the triangle with vertices at the point given in the fol...

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  13. Find area of the triangle with vertices at the point given in the fol...

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  14. Show that points A(a,b+c),B(b,c+a) ਅਤੇ C(c,a+b) are collinear.

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  15. Find the value of k if the area of the triangle is 4 sq. units whose v...

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  16. If area of triangle is 4 sq. units with vertices (-2, 0), (0, 4) and (...

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  17. Find equation of line joining (1, 2) and (3, 6) using determinants.

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  18. Find equation of line joining (3, 1) and (9, 3) using determinants.

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  19. If area of triangle is 35 sq. units with vertices (2,-6), (5, 4) and (...

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  20. Write Minors and Cofactors of the elements of following determinant : ...

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