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Using properties of determinants prove ...

Using properties of determinants prove the
following.
`abs[[b+c,a,a],[b,c+a,b],[c,c,a+b]]=4abc`

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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)

Using properties of determinants prove the following. abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

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)

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) .

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)

By using properties of determinants, prove that |[-a^2,ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]|=4a^2b^2c^2

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

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

Using properties of determinants, prove that |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]| = 3(a+b+c)(ab+bc+ca)

Without expanding the determinant prove the following. |[a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c]|=0

V PUBLICATION-DETERMINANT-QUESTION BANK
  1. Without expanding prove that abs[[x+y,y+z,z+x],[z,x,y],[1,1,1]]=0

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  2. Evaluate Delta=|[1, a, bc],[ 1, b, c a],[ 1, c, a b]|

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  3. Using properties of determinants prove the following. abs[[b+c,a,...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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