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Without expanding prove that abs[[x+y,...

Without expanding prove that
`abs[[x+y,y+z,z+x],[z,x,y],[1,1,1]]=0`

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prove that abs[[a,b,c],[a+2x,b+2y,c+2z],[x,y,z]]=0

Prove that abs[[1,x,x^2],[1,y,y^2],[1,z,z^2]]=(x-y)(y-z)(z-x)

Without expanding the determinant prove the following. |[x,a,x+a],[y,b,y+b],[z,c,z+c]|=0

By using properties of determinants, prove that |[x+y+2z,x,y],[z,y+z+2x,y],[z,x,z+x+2y]|=2(x+y+z)^3

By using properties of determinants, prove that |[x,x^2,yz],[y,y^2,zx],[z,z^2,xy]|=(x-y)(y-z)(z-x)(xy+yz+zx)

Find the value of x,y and z from the equation: [[x+y+z], [x+z],[y+z]]=[[9],[5],[7]]

Consider the determinant Delta=abs[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,1+z^3]] , Where x,y,z are different. Show that if Delta=0 ,then 1+xyz=0

Consider the determinant Delta=abs[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,1+z^3]] , Where x,y,z are different. Express the above determinant as sum of two determinants.

Find the value of x,y and z from the equation: [[4,3],[x,5]]=[[y,z],[1,5]]

Without expanding the determinant prove the following. |[b+c,q+r,y+z],[c+a,r+p,z+x],[a+b,p+q,x+y]|=2|[a,p,x],[b,q,y],[c,r,z]|

V PUBLICATION-DETERMINANT-QUESTION BANK
  1. prove that abs[[a,b,c],[a+2x,b+2y,c+2z],[x,y,z]]=0

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  2. Prove that |[a, a+b, a+b+c],[ 2 a, 3 a+2 b, 4 a+3 b+2 c],[ 3 a, ...

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  3. Without expanding prove that abs[[x+y,y+z,z+x],[z,x,y],[1,1,1]]=0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. 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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