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By using properties of determinants, sh...

By using properties of determinants, show that : `|[1,a,a^2],[1,b,b^2],[1,c,c^2]| = (a-b)(b-c)(c-a)`

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By using properties of determinants, show that : |[1,1,1],[a,b,c],[a^3,b^3,c^3]| = (a-b)(b-c)(c-a)(a+b+c)

Using the properties of determinant, show that : |[1,a+b,a^2+b^2],[1,b+c,b^2+c^2],[1,c+a,c^2+a^2]| = (a-b)(b-c)(c-a)

Using the properties of determinants show that : |[[1,1,1],[a^2,b^2,c^2],[a^3,b^3,c^3]]|=(a-b)(b-c)(c-a)(ab+bc+ca) .

Using the properties of determinants show that : |[[1, a^2+bc, a^3],[1,b^2+ac,b^3],[1,c^2+ab,c^3]]|=(a-b)(b-c)(c-a)(a^2+b^2+c^2)

Using the properties of determinants show that : |[[a^2, b^2, c^2],[bc,ca,ab],[a,b,c]]|=(a-b)(b-c)(c-a)(ab+bc+ca)

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

By using properties of determinants, Show that : {:|(0,a,-b),(-a,0,-c),(b,c,0)|=0

Prove that |[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-ab]|= 0

PSEB-DETERMINANTS-Exercise
  1. Using the property of determinants and without expanding , prove that:...

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  2. Prove that: |[-a^2, ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]|=4a^2b^2c^2

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  3. By using properties of determinants, show that : |[1,a,a^2],[1,b,b^2]...

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  4. By using properties of determinants, show that : |[1,1,1],[a,b,c],[a^...

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

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

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

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

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

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

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  13. Which of the following is correct

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

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

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

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

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

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

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

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