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Prove that abs[[y+k,y,y],[y,y+k,y],[y,...

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

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

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

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

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MAXIMUM PUBLICATION-DETERMINANTS-EXAMPLE
  1. Consider the following system of linear equations, x+y+z=6,x-y+z=2, ...

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  2. If abs[[x,3],[5,2]]=5,then x=…..

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

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  4. Solve the following system of linear Equations,using matrix method, ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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