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Show that abs[[1,a,a^2],[1,b,b^2],[1,c...

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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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) .

Show that abs [[1,a,bc],[1,b,ac],[1,c,ab]]=(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)

Prove that |[1 , a , a^3],[ 1, b, b^3],[ 1, c, c^3]|=(a-b)(b-c)(c-a)(a+b+c)

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[[1,1,1],[a,b,c],[a^3,b^3,c^3]]=(a-b)(b-c)(c-a)(a+b+c)

Show that Delta=abs[[-a^2,ab,ac],[ba,-b^2,bc],[ac,bc,-c^2]]=4a^2b^2c^2

Using properties of determinants show that abs[[1+a,1,1],[1,1+b,1],[1,1,1+c]]=abc(1+1/a+1/b+1/c)

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

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

MAXIMUM PUBLICATION-DETERMINANTS-EXAMPLE
  1. If A=[[1,1,5],[0,1,3],[0,-1,-2]] what is the value of abs[3A]?

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  2. Find the equation of the line joining the points(1,2) and (-3,-2) us...

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  3. 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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  4. Consider the following system of linear equations, x+y+z=6,x-y+z=2, ...

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  5. Consider the following system of linear equations, x+y+z=6,x-y+z=2, ...

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  6. Consider the following system of linear equations, x+y+z=6,x-y+z=2, ...

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  7. If abs[[x,3],[5,2]]=5,then x=…..

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

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

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

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

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

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

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

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

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

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

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

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

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