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Prove that abs[[1,x,x^2],[1,y,y^2],[1,z,...

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

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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)

Prove that |(1,x,x^3),(1,y,y^3),(1,z,z^3)|=(x+y+z)(x-y)(y-z)(z-y) .

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

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

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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.

Prove that |(x^(2),x^(2)-(y-z)^(2),yz),(y^(2),y^(2)-(z-x)^(2),zx),(z^(2),z^(2)-(x-y)^(2),xy)|=(x-y)(y-z)(z-x)(x+y+z)(x^(2) + y^(2) + z^(2)) .

Given Delta=|(x,x^2,1+px^3),(y,y^2,1+py^3),(z,z^2,1+pz^3)| Prove that Delta=(1+pxyz)(x-y)(y-z)(z-x) .

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MAXIMUM PUBLICATION-DETERMINANTS-EXAMPLE
  1. Solve the following system of linear Equations,using matrix method, ...

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  2. Let B is a square matrix of order 5, then abs[kB] is equal to….

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

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  4. Check the consistency of the following equations, 2x+3y+z=6,x+2y-z...

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  5. Find the values of x in which abs[[3,x],[x,1]]=abs[[3,2],[4,1]]

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

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  7. Examine the consistency of system of following equations: 5x-6y+4z...

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  8. Consider a system of linear equations which is given below, 2/x+3/y+10...

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  9. Consider a system of linear equations which is given below, 2/x+...

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  10. Consider a system of linear equations which is given below, 2/x+3/...

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  11. Consider the matrices A=[[2,3],[4,5]] Prove thatA^2-7A-2I=0

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  12. Consider the matrices A=[[2,3],[4,5]] Hence find A^-1

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  13. Consider the matrices A=[[2,3],[4,5]] Solve the following system of ...

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

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

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  16. Examine the consistency of the system of Equations. 5x+3y=5,2x+6y=...

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  17. Choose the correct statement related to the matrices A=[[1,0],[0,1]]...

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  18. IfM=[[7,5],[2,3]],then verify the equation M^2-10M+11I2=0

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  19. Inverse of the matrix [[0,1,2],[0,1,1],[1,0,2]]

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  20. Solve the system of Linear equations x+2y+z=8,2x+y-z=1,x-y+z=2

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