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Using properties of determinants show ...

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)`

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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) .

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

The value of the determinant abs[[1,1,1],[1,-1,-1],[1,1,-1]] is

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

By using the properties of determinants,prove that |[a^2+1,ab ,ac],[ab,b^2+1,bc],[ca ,cb,c^2+1]|=1+a^2+b^2+c^2

By using the properties of determinants,prove that |[1+a^2-b^2,2ab ,-2b],[2ab,1-a^2+b^2,2a],[2b ,-2a,1-a^2-b^2]|=(1+a^2+b^2)^3

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V PUBLICATION-DETERMINANT-QUESTION BANK
  1. Using properties of determinants prove the following. abs[[b+c,a,...

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  2. Consider the determinant Delta=abs[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,...

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  3. Using properties of determinants show that abs[[1+a,1,1],[1,1+b,1]...

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  4. Without expanding the determinant prove the following. |[x,a,x+a],[y...

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  5. Without expanding the determinant prove the following. |[a-b,b-c,c-a...

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  6. Evaluate |[2, 7, 65],[ 3, 8, 75],[ 5, 9, 86]|=0

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  7. prove |[1, b c, a(b+c)],[ 1, c a, b(c+a)],[ 1, a b, c(a+b)]|=0

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  8. Without expanding the determinant prove the following. |[b+c,q+r,y+z...

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  9. By using properties of determinants, prove that |[0,a ,-b],[-a,0,-c],...

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

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

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

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

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

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

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

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

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

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