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Show that abs[[1,a,a^2],[1,b,b^2],[1,c...

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`abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a)`

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using properties of determinants, prove that abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a) .

Show that abs [[1,a,bc],[1,b,ac],[1,c,ab]]=(a-b)(b-c)(c-a)

Using properties of determinants, show that abs[[a,a^2,b+c],[b,b^2,c+a],[c,c^2,a+b]]=(b-c)(c-a)(a-b)(a+b+c)

Prove that |[1 , a , a^3],[ 1, b, b^3],[ 1, c, c^3]|=(a-b)(b-c)(c-a)(a+b+c)

Using properties of determinants prove the following. abs[[1,a,bc],[1,b,ca],[1,c,ab]]=(a-b)(b-c)(c-a)

Using properties of determinants prove the following. abs[[1,1,1],[a,b,c],[a^3,b^3,c^3]]=(a-b)(b-c)(c-a)(a+b+c)

Show that Delta=abs[[-a^2,ab,ac],[ba,-b^2,bc],[ac,bc,-c^2]]=4a^2b^2c^2

Using properties of determinants show that abs[[1+a,1,1],[1,1+b,1],[1,1,1+c]]=abc(1+1/a+1/b+1/c)

Prove that abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

Prove that abs[[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]] =2abc(a+b+c)^3

V PUBLICATION-DETERMINANT-QUESTION BANK
  1. By using properties of determinants, prove that |[0,a ,-b],[-a,0,-c],...

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  2. By using properties of determinants, prove that |[-a^2,ab,ac],[ba,-b^...

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  3. Show that abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a)

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  4. By using properties of determinants, prove that |[x,x^2,yz],[y,y^2,zx...

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  5. Prove that abs[[y+k,y,y],[y,y+k,y],[y,y,y+k]]=k^2(3y+k)

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

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  7. Using properties of determinants prove the following. abs[[1,x,x^2...

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  8. Prove |[1+a^2-b^2, 2 a b, -2 b],[ 2 a b, 1-a^2+b^2, 2 a],[ 2 b,...

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  9. By using the properties of determinants,prove that |[a^2+1,ab ,ac],[a...

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  10. Let A be a square matrix of order 2x2 thenabs[KA] is equal to

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  11. Which of the following is correct? a)Determinant is a square matrix ...

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  12. Find the area of the triangle whose vertices are (3,8),(-4,2)and (5,1)

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  13. Find the equation of the line joining A(1,3) and B(0,0) using determin...

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  14. Find the area of the triangle with vertices at (1,0),(6,0),(4,3) using...

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  15. Using the property of determinants,show that the points A(a,b+c),B(b...

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  16. Find the values of k if area of triangle is 4 sq. units and vertices a...

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

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

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  19. Find the minor of 1 in the determinant Delta=|[3, 4, 5 ],[2, 7, 1]...

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  20. Find minors of element 6 in the determinant Delta=|[ 1, 2, 3],[ 4, ...

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