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

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

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Find the values of x, y, z , if the matrix A=[[0, 2 y, z],[ x, y, -z],[ x, -y, z]] satisfy the equation A^' A=I

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)

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

If x + y + z = 0 , prove that |(ax,by,cz),(cy,az,bx),(bz,cx,ay)|=xyz|(a,b,c),(c,a,b),(b,c,a)|

Show that Delta=|[(y+z)^2, x y , z x],[ x y, (x+z)^2, y z],[ x z, y z, (x+y)^2]|=2 x y z(x+y+z)^3

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

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. Evaluate Delta=|[3, 2, 3],[ 2, 2, 3],[ 3, 2, 3]|

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  2. Evaluate |[102, 18, 36],[ 1, 3, 4],[ 17, 3, 6]|

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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